Assam Board Class 11 Logic and Philosophy – Unit 3:Inference, Categorical Syllogism MCQs and Complete Solution
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Unit 3
The short and long questions from this chapter given in the last 10 years are:
1. State any two rules of obversion? (2 Mark, 2012) ✅
Answer:
The quality of the proposition must be changed (affirmative to negative or vice versa).
The predicate must be replaced by its complement.
2. Write the rule of inverse variation? (2 Mark, 2012) ✅
Answer:
In an inverse variation, when one quantity increases, the other decreases proportionally.
It is mathematically represented as: x ∝ 1/y or x × y = constant.
3. State three characteristics of deductive inference. (3 Mark, 2012) ✅
Answer:
Deductive reasoning moves from general to specific.
If the premises are true, the conclusion must be true.
It follows a logical structure and is often used in mathematics and logic.
4. What is obversion? Convert the following proposition: "No man is perfect." (4 Mark, 2012) ✅
Answer:
Obversion is an immediate inference in which the quality of a proposition is changed, and the predicate is replaced with its complement.
Given Proposition: "No man is perfect."
Obverted Form: "All men are imperfect."
5. Give an example of conversion. (2 Mark, 2012) ✅
Answer:
Original Proposition: "All cats are animals."
Converted Form: "Some animals are cats."
6. 'Man is not mortal' – reduce this sentence into proper logical form and give its obverse. (3 Mark, 2013) ✅
Answer:
Logical Form: "No man is mortal."
Obverse: "All men are immortal."
7. What is immediate inference? Give an example. (3 Mark, 2014) ✅
Answer:
Immediate inference is a type of reasoning where a conclusion is drawn directly from a single premise without using a second premise.
Example:
Premise: "All birds are animals."
Inference: "Some animals are birds."
8. In an immediate inference, how many premises are there? (1 Mark, 2015) ✅
Answer:
There is only one premise in an immediate inference.
9. State one point of difference between immediate inference and mediate inference. (2 Mark, 2015) ✅
Answer:
Immediate inference requires only one premise, whereas mediate inference requires at least two premises.
10. State two characteristics of deductive inference. (2 Mark, 2015) ✅
Answer:
Deductive reasoning moves from general to specific conclusions.
If the premises are true, the conclusion must be true.
11. Define mediate inference. (2 Mark, 2017) ✅
Answer:
Mediate inference is reasoning where a conclusion is drawn from two or more premises using logical principles.
12. Give a definition of observation. (2 Mark, 2017) ✅
Answer:
Observation is the process of gathering knowledge through sensory perception without inference.
13. State any two rules of conversion. (2 Mark, 2011) ✅
Answer:
The subject and predicate must be interchanged.
The quantity of the proposition must not be increased.
14. 'Vaishnavas are also Hindus' – reduce this sentence into proper logical form and give its converse. (3 Mark, 2011) ✅
Answer:
Logical Form: "All Vaishnavas are Hindus."
Converse: "Some Hindus are Vaishnavas."
15. Name any one of the fundamental Laws of Thought. (1 Mark, 2011) ✅
Answer:
The Law of Identity: "Whatever is, is."
16. 'In inductive inference, the conclusion necessarily follows from the premises.' Is it true? (1 Mark, 2018) ✅
Answer:
No, inductive inference is probabilistic, meaning the conclusion is likely but not necessarily true.
17. What is material truth? Give an example. (2 Mark, 2018) ✅
Answer:
Material truth means a proposition is factually correct, regardless of logical structure.
Example: "Water boils at 100°C at sea level."
18. State any two points of difference between deductive and inductive inference. (2 Mark, 2018) ✅
Answer:
Deductive inference moves from general to specific, whereas inductive inference moves from specific to general.
Deductive conclusions are certain, while inductive conclusions are probable.
19. Give the converse and obverse of the proposition: "No men are gods." (2 Mark, 2018) ✅
Answer:
Converse: "No gods are men."
Obverse: "All men are non-gods."
20. What is obversion? State any three rules of obversion. (4 Mark, 2018) ✅
Answer:
Obversion is an immediate inference where the quality of the proposition is changed, and the predicate is replaced by its complement.
Three Rules of Obversion:
Change the quality (affirmative to negative or vice versa).
Replace the predicate with its complement.
The quantity of the proposition remains unchanged.
21. Give the converse and obverse of the proposition: "No men are gods." (1+1 = 2 Mark, 2018) ✅
Answer:
Converse: "No gods are men."
Obverse: "All men are non-gods."
Additional 1 Marks Question
1. In an immediate inference, how many premises are there? (1 Mark, 2015) ✅
Ans. 1 (one).
2. Name any one of the fundamental laws of thought. (1 Mark, 2012) ✅
Ans. The Law of Identity.
3. "In inductive inference, the conclusion necessarily follows from the premises." Is it true? (1 Mark, 2018) ✅
Ans. No.
4. "In deductive inference, the conclusion necessarily follows from the premises." Is it true? (1 Mark) ✅
Ans. Yes, it is true.
5. Inference is a process from known to unknown / unknown to known. (1 Mark) ✅
Ans. Known to unknown.
6. Inference is a process from universal to particular / particular to universal. (1 Mark) ✅
Ans. Both.
7. There is one / two / three premises in an immediate inference. (1 Mark) ✅
Ans. One.
8. Immediate inference is a kind of induction / deduction. (1 Mark) ✅
Ans. Deduction.
9. There are two / three / two or more premises in a mediate inference. (1 Mark) ✅
Ans. Two or more.
10. Broadly, inference is divided into two / four kinds. (1 Mark) ✅
Ans. Two.
11. It is possible / impossible to make simple conversion of an 'A' proposition. (1 Mark) ✅
Ans. Impossible.
MCQs
1. What is the process of drawing a conclusion based on premises called?
(i) Reasoning.
(ii) Inference.
(iii) Argument.
(iv) Experimentation.
Ans: (ii) Inference.
2. Which of the following represents the premises in an argument?
(i) Conclusion.
(ii) Supporting propositions.
(iii) Statements.
(iv) Inference.
Ans: (ii) Supporting propositions.
3. When an inference is expressed in language, it is called:
(i) Argument.
(ii) Conclusion.
(iii) Statements.
(iv) Inference.
Ans: (i) Argument.
4. Which type of categorical proposition affirms the membership of all subjects in a class?
(i) A proposition.
(ii) E proposition.
(iii) I proposition.
(iv) O proposition.
Ans: (i) A proposition.
5. Which of the following propositions are so related that they cannot both be false although they may both be true, as per square of opposition?
(i) Some apes are monkeys.
(ii) Some apes are not monkeys.
(iii) (i) and (ii) only.
(iv) None of the above.
Ans: (iii) (i) and (ii) only.
6. How many terms are there in a valid categorical syllogism?
(i) 3
(ii) 4
(iii) 2
(iv) 5
Ans: (i) 3
7. Which type of inference starts from general premises and leads to a particular conclusion?
(i) Inductive inference.
(ii) Deductive inference.
(iii) Immediate inference.
(iv) Mediate inference.
Ans: (ii) Deductive inference.
8. All Judges are fair minded’ is an example of _____________ proposition.
(i) Universal affirmative.
(ii) Universal negative.
(iii) Particularly affirmative.
(iv) Particularly negative.
Ans: (i) Universal affirmative.
9. In deductive inference, the conclusion is always:
(i) Conclusion is true in all such cases.
(ii) Less general or equally general as the premises.
(iii) Deductive arguments may be said to be valid or invalid.
(iv) Contradictory to the premises.
Ans: (ii) Less general or equally general as the premises.
10. What do we call an argument with more than one premise?
(i) Major premise inference.
(ii) Mediate inference.
(iii) Minor premise inference.
(iv) None of the above.
Ans: (ii) Mediate inference.
11. Which of the following forms of categorical Proposition is valid?
(i) Some S are not P.
(ii) Some S is P.
(iii) No S is P.
(iv) All S is P.
Choose the correct answer from the options given below:
(i) A, B, C and D.
(ii) B, C and D Only.
(iii) A, C and D Only.
(iv) A, B and D Only.
Ans: (i) A, B, C and D.
12. In conversion, what happens in the inference process?
(i) Proposition changes.
(ii) Subject and predicate are swapped.
(iii) Immediate inference.
(iv) None of the above.
Ans: (ii) Subject and predicate are swapped.
13. In the statement “No dogs are reptiles”, which terms are distributed?
(i) Only subject term.
(ii) Only predicate terms.
(iii) Both subject and predicate terms.
(iv) Neither subject nor predicate term.
Ans: (iii) Both subject and predicate terms.
14. What is the conclusion in the following syllogism? All men are mortal. All poets are men. Therefore, all poets are mortal.
(i) All men are mortal.
(ii) All poets are mortal.
(iii) All poets are men.
(iv) Men are mortal.
Ans: (ii) All poets are mortal.
15. Which of the following propositions is logically equivalent to the proposition – “All frogs are amphibians”?
(i) No amphibians are non-frogs.
(ii) No frogs are non-amphibians.
(iii) Some amphibians are frogs.
(iv) Some amphibians are not frogs.
Ans: (ii) No frogs are non-amphibians.
Questions and Answers (Mark: 2)
1. State any two points of difference between deductive and inductive inference. (2 Mark, 2018) ✅
Ans.
(i) Deductive inference moves from universal premises to a particular conclusion, while inductive inference moves from particular premises to a general conclusion.
(ii) In deductive inference, the conclusion necessarily follows from the premise(s), but in inductive inference, it does not necessarily follow.
2. What is material truth? Give an example. (2 Mark, 2018) ✅
Ans. The correspondence of our ideas or thoughts with actually existing facts is called material truth.
Example: "Green leaves of a tree" is a statement of material truth.
3. Give the converse and obverse of the proposition: "No men are gods." (2 Mark, 2018) ✅
Ans.
Converse: "No gods are men." (E)
Obverse: "All men are not gods." (A)
4. State any two rules of obversion. (2 Mark, 2012) ✅
Ans.
(i) The subject of the obverse remains the same as that of the obvertend.
(ii) The predicate of the obverse is the contradictory of the predicate of the obvertend.
5. Give an example of conversion. (2 Mark, 2012) ✅
Ans.
Given Proposition: "All men are mortal." (A)
Converted Form: "Some mortal beings are men." (I)
6. State one point of difference between immediate inference and mediate inference. (2 Mark, 2015) ✅
Ans. In immediate inference, the conclusion is drawn from only one premise, whereas in mediate inference, the conclusion is drawn from two or more premises.
7. Give a definition of obversion. (2 Mark, 2011) ✅
Ans. Obversion is an immediate inference where the quality of the proposition is changed, while the meaning remains the same.
8. State any two rules of conversion. (2 Mark, 2011) ✅
Ans.
(i) The subject and predicate must be interchanged.
(ii) The quantity of the proposition must not be increased.
9. Define mediate inference. (2 Mark, 2017) ✅
Ans. An inference in which the conclusion is drawn from two or more premises is called mediate inference.
Example:
Premise 1: "All men are mortal."
Premise 2: "Ram is a man."
Conclusion: "Ram is mortal."
10. State two characteristics of deductive inference. (2 Mark, 2013) ✅
Ans.
(i) The conclusion follows from one or more premises.
(ii) The aim of deductive inference is to prove the formal truth or consistency.
11. Define inference. (2 Mark) ✅
Ans. Inference is a mental process through which we proceed from the known to the unknown.
12. Define deductive inference. (2 Mark) ✅
Ans. Deductive inference is one in which the conclusion cannot be more general than the premise(s).
13. What do you mean by mediate inference? (2 Mark) ✅
Ans. Mediate inference is one in which the conclusion is drawn from two or more premises.
14. What is immediate inference? (2 Mark) ✅
Ans. Immediate inference is one in which the conclusion is drawn from a single premise.
15. Define conversion. (2 Mark) ✅
Ans. Conversion is a type of immediate inference in which the subject and predicate of a proposition are interchanged without changing its truth value.
16. What is simple conversion? (2 Mark) ✅
Ans. Simple conversion is a type of immediate inference in which the quantity of the converse remains the same as the convertend.
17. Define material obversion. (2 Mark) ✅
Ans. Material obversion is the process of changing the quality of a proposition while maintaining its meaning.
Here’s your organized question and answer format with a green tick (✅) after each year-marked question:
18. What is material obversion? (2 Mark) ✅
Ans. Material obversion is the process of drawing an obverse inference that is justified only when examining the matter of the proposition.
19. Give an example of obversion of an 'A' proposition. (2 Mark) ✅
Ans.
Given Proposition ('A'): "All men are mortal."
Obverted Form ('E'): "No men are immortal."
20. Give an example of deductive inference. (2 Mark) ✅
Ans.
Premise 1: "All men are mortal."
Premise 2: "Biva is a man."
Conclusion: "Biva is mortal."
21. State an example of inductive inference. (2 Mark) ✅
Ans.
Observation 1: "Ram is mortal."
Observation 2: "Hari is mortal."
Observation 3: "Krishna is mortal."
Conclusion: "All men are mortal."
22. Give an example of immediate inference. (2 Mark) ✅
Ans.
Given Proposition: "All men are mortal."
Immediate Inference: "Some mortal beings are men."
23. Mention an example of mediate inference. (2 Mark) ✅
Ans.
Premise 1: "No man is perfect."
Premise 2: "Jadu is a man."
Conclusion: "Jadu is not perfect."
24. Give an example of conversion. (2 Mark) ✅
Ans.
Given Proposition: "No man is immortal."
Converted Form: "No immortal being is a man."
25. Give the converse and obverse of the proposition: "No men are gods." (2 Mark, 2018) ✅
Ans.
Converse: "No gods are men."
Obverse: "All men are not gods."
Questions and Answers (Mark: 3)
1. "Man is not mortal" – Reduce this sentence into proper logical form and give its obverse. (3 Mark,2013) ✅
Ans.
Logical Form: "No man is mortal."
Obverse: "All men are immortal."
2. State three characteristics of deductive inference. (3 Mark, 2012) ✅
Ans.
(i) In deductive inference, the conclusion follows from one or more premises.
(ii) The conclusion cannot be more general than the premises, as it necessarily follows from them.
(iii) The conclusion is implicitly contained in the premises, making it logically necessary.
3. "Vaisnavas are also Hindus." Reduce this sentence into proper logical form and give its converse. (3 Mark, 2014) ✅
Ans.
Logical Form: "All Vaisnavas are Hindus." (A)
Converse: "Some Hindus are Vaisnavas." (I)
4. What is inference? Give an example. (3 Mark) ✅
Ans. Inference is the process of deriving a conclusion from one or more given premises.
Example:
Premise 1: "All smoky objects are fiery."
Premise 2: "The hill is smoky."
Conclusion: "The hill is fiery."
5. Define argument with an example. (3 Mark) ✅
Ans. An argument is a set of statements (propositions) where one statement (the conclusion) is claimed to follow from the others (premises).
Example:
Premise 1: "All men are mortal."
Premise 2: "All scientists are men."
Conclusion: "All scientists are mortal."
6. Define immediate inference with an example. (3 Mark, 2014) ✅
Ans. An immediate inference is an inference drawn from a single premise.
Example:
Given Proposition: "All men are mortal."
Immediate Inference: "Some mortal beings are men."
7. Define mediate inference with an example. (3 Mark, 2013) ✅
Ans. A mediate inference is an inference in which the conclusion is drawn from two or more premises.
Example:
Premise 1: "All men are mortal."
Premise 2: "Jadu is a man."
Conclusion: "Jadu is mortal."
8. Can an 'O' proposition be converted? (3 Mark, 2013) ✅
Ans. No, an 'O' proposition cannot be converted.
Example:
Given Proposition (O): "Some poets are not philosophers."
Issue: The subject term ('poet') is not distributed in the converse, so an 'O' proposition cannot be converted.
9. Define simple conversion with an example. (3 Mark) ✅
Ans. Simple conversion is a type of conversion in which the quantity of the conclusion remains the same as that of the premise.
Example:
Given Proposition (I): "Some men are philosophers."
Converted Form (I): "Some philosophers are men."
10. Define obversion with an example. (1 Mark) ✅
Ans. Obversion is a type of immediate inference in which the quality of the proposition is changed, but its meaning remains the same.
Example:
Given Proposition ('A'): "All men are mortal."
Obverted Form ('E'): "No men are non-mortal."
11. Distinguish between inductive and deductive inference. (3 Mark, 2013) ✅
Ans.Distinguish between Inductive and Deductive Inference…
Questions and Answers (Mark: 4/5)
1. What is obversion? Convert the following proposition: "No man is perfect." (4 Mark, 2012) ✅
Ans.
Obversion is a type of immediate inference in which the quality of the proposition is changed, and the predicate is replaced by its contradictory, while the meaning remains unchanged.
Given Proposition ('E'): "No man is perfect."
Obverted Form ('A'): "All men are imperfect."
2. State four rules of conversion. (4 Mark) ✅
Ans. The rules of conversion are as follows:
(i) The subject of the converted statement becomes the predicate of the converse.
(ii) The predicate of the converted statement becomes the subject of the converse.
(iii) The quality of the converse remains the same as that of the convertend.
(iv) No term can be distributed in the converse unless it was distributed in the convertend.
3. State four rules of obversion. (4 Mark) ✅
Ans. The rules of obversion are:
(i) The subject of the obverse remains the same as that of the obvertend.
(ii) The predicate of the obverse is the contradictory of the predicate of the obvertend.
(iii) The quality of the obverse must be changed from affirmative to negative or vice versa.
(iv) The quantity of the obverse remains the same as that of the obvertend.
4. State four characteristics of a deductive argument. Expand. (4 Mark) ✅
Ans. The four main characteristics of a deductive argument are:
Logical Necessity:
In a deductive argument, the conclusion necessarily follows from the premises. If the premises are true, the conclusion must also be true.
Moves from General to Specific:
Deductive reasoning always moves from a universal/general rule to a specific conclusion.
No New Information:
The conclusion does not introduce new information; it is already implicitly contained in the premises.
Validity and Soundness:
A deductive argument can be valid (logically correct) or invalid. It is considered sound only if both the premises are true and the argument is valid.
5. Mention four rules of inductive argument? (4 Mark) ✅
Ans. The four rules of inductive argument are:
The Conclusion Follows from More Than One Premise:
In inductive reasoning, conclusions are derived from multiple observations or premises. It involves generalizing from a set of premises that provide support, but not certainty, for the conclusion.
Conclusion Does Not Necessarily Follow from Premises:
Unlike deductive arguments, where the conclusion must follow from the premises, in inductive reasoning, the conclusion may or may not necessarily follow. The premises provide a high degree of probability, but not certainty.
The Conclusion Is More General Than the Premises:
The conclusion of an inductive argument is usually broader or more general than the premises. For instance, specific observations are used to make a general statement about a group or phenomenon.
Truth of Premises Cannot Prove the Truth of the Conclusion:
Inductive reasoning works by drawing conclusions from observed patterns or examples, but since the conclusion goes beyond the premises, it does not guarantee the truth of the conclusion even if the premises are true. The conclusion is probable, not certain.
6. What is conversion? State the rules of conversion. (5 Mark) ✅
Ans.
Conversion is a type of immediate inference in which the subject and predicate of the proposition are swapped, and the logical relationship between them is maintained.
For example:
Original Proposition (A): "All men are mortal."
Converse Proposition (I): "Some mortal beings are men."
Rules of Conversion:
(i) Subject of the Convertend Becomes the Predicate in the Converse:
In conversion, the subject of the original statement becomes the predicate in the converse.
(ii) The Quality of the Convertend and Converse is the Same:
The quality (affirmative or negative) of both the original and converse remains the same.
(iii) The Predicate of the Convertend Becomes the Subject in the Converse:
The predicate in the original statement becomes the subject in the converted statement.
(iv) No Term Can Be Distributed in the Converse Without Being Distributed in the Convertend:
For the conversion to be valid, no term can be distributed in the converse unless it was already distributed in the original statement.
7. What is obversion? State the rules of obversion. (4/5 Mark, 2018) ✅
Ans.
Obversion is a type of immediate inference where the quality of the proposition is changed, and the predicate is replaced by its contradictory, while the meaning remains unchanged.
Example:
Original Proposition ('A'): "All men are mortal."
Obverted Proposition ('E'): "No men are non-mortal."
Rules of Obversion:
(i) Subject of the Obverse Remains the Same as That of the Obvertend:
In obversion, the subject of the obverse proposition is the same as the subject of the original (obvertend) proposition.
(ii) Predicate of the Obverse Will Be the Contradictory of the Obvertend's Predicate:
The predicate of the obverse becomes the contradictory of the original predicate (i.e., replacing terms like "mortal" with "non-mortal").
(iii) Quality of the Obverse Will Be Different from That of the Obvertend:
The quality of the obverse is the opposite of the quality of the original statement. If the original statement is affirmative, the obverted statement will be negative, and vice versa.
(iv) The Quantity of the Obverse Will Be the Same as That of the Obvertend:
The quantity (whether universal or particular) of the obverse remains the same as that of the original proposition.
-0000-
Categorical Syllogism
Write the name of any one valid mood of the third figure. (1 Mark, 2012) ✅
What is the nature of copula? (1 Mark, 2012, 2014) ✅
Give definition and example of syllogism. (4 Mark, 2012) ✅
Test the validity of the following argument. (1 Mark, 2012) ✅
State five general rules of pure categorical syllogism. (5 Mark, 2012) ✅
What is the name of the subject of the conclusion of a syllogism? (1 Mark, 2013) ✅
What is the role of the middle term in a syllogism?
Test the following arguments. (4 Mark, 2013, 2014, 2015) ✅
How many terms are there in a syllogism? (1 Mark, 2014, 2016) ✅
What do you mean by the figure of syllogism? How many types of figure of syllogism, discuss. (4 Mark, 2014)
How many valid moods are there in the fourth figure? (1 Mark, 2011)
What do you mean by the figure of syllogism? (2 Mark, 2011, 2016) ✅
Prove that in the second figure one of the premises must be negative?
Test the following argument. (4 Mark, 2011) (4 Mark, 2013) ✅
What is the position of the middle term in the second figure of syllogism?
How is the figure of a syllogism determined? (1 Mark, 2012) ✅
What do you mean by the mood of a syllogism? (1 Mark, 2015, 2017) ✅
State four characteristics of a categorical syllogism. (4 Mark, 2015) (2 Mark, 2015) ✅
19. Reduce any one of the following syllogistic arguments into logical form and test whether it is valid or invalid.
(a) All men are not industrious but he is industrious, so he cannot be a man.
20. What is the name of the subject of the conclusion of a syllogism?
(1 Mark, 2016) ✅
21. How many valid moods are there in the second figure of a syllogism?
22. Define syllogism. State three general rules of categorical syllogism.
(2 Mark, 2016)
23. Test the validity of any one of the following.
(a) My arm touches the table. The table touches the floor. Therefore, my arm touches the floor.
(b) All Assamese are intelligent, All Marathis are intelligent. Therefore, all Marathis are Assamese.
24. How many valid moods are there in the third figure of a syllogism?
(1 Mark, 2017)
25. What is the name of the predicate of the conclusion of a syllogism?
(4 Mark, 2015) ✅
26. Name two valid moods of the fourth figure.
(1 Mark, 2017)
27. Give an example of syllogism.
(2 Mark, 2017)
28. Describe the structure of categorical syllogism.
(2 Mark, 2013)
29. Test the validity of the following arguments.
(a) We are dependent on our cars, our cars are dependent on drivers, therefore, we are dependent on drivers.
(b) Only honest persons are happy; John is honest, therefore, John is happy.
(4 Mark, 2013) ✅
30. What is the position of the middle term in the second figure of a syllogism?
(1 Mark, 2018)
31. State any two general rules of pure categorical syllogism.
32. Give an example of BARBARA.
33. Reduce any one of the following syllogistic arguments into logical form and test its validity: (4 Mark, 2018)
(a) All men are not industrious, he is industrious. Therefore, he is not a man.
(b) My arm touches the table, the table touches the floor, therefore, my arm touches the floor.
34. How is the figure of syllogism determined? (1 Mark, 2017) ✅
Questions and Answers(1 Mark):
1. What is the name of the predicate of the conclusion of a syllogism? (1 Mark, 2017) ✅
Ans: Major term.
2. How many valid moods are there in the third figure of a syllogism? (1 Mark, 2017) ✅
Ans: Six.
3. What is the position of the middle term in the second figure of a syllogism? (1 Mark, 2012, 2018) ✅
Ans: Predicate term of both premises.
4. What is the name of the subject of the conclusion of the syllogism? (1 Mark, 2016)
Ans: Minor terms.
5. How is the figure of a syllogism determined? (1 Mark, 2015, 2017) ✅
Ans: Position of the middle term.
6. How many valid moods are there in the fourth figure? (2 Mark, 2018) ✅
Ans: Five (5).
7. How many valid moods are there in the fourth figure? (2 Mark, 2017) ✅
Ans: Three (3).
8. How many terms are there in a syllogism? (1 Mark, 2014)
9. Write the name of any one valid mood of the third figure.
Ans: DARAPTI. (1 Mark, 2012) ✅
10. What is the nature of Copula?
Ans: (i) The copula may be either affirmative or negative. (ii) The copula must be used in the present tense.
11. FERIO is a valid mood of ___ figure.
Ans: 1st figure. (1 Mark, 2016) ✅
12. How many valid moods are there in the second figure of syllogism? (1 Mark, 2016) ✅
Ans: Four (4).
13. What are the basic kinds of syllogism?
Ans: (i) Mixed syllogism (ii) Pure syllogism.
14. Are all the three propositions categorical in a categorical syllogism?
Ans: Yes. (1 Mark, 2013) ✅
15. What type of relation is there in the proposition in categorical syllogism?
Ans: Categorical.
16. How many propositions are in a syllogism? (1 Mark, 2015) ✅
Ans: Three.
17. Write two names of the valid moods of the first figure? (1 Mark, 2012, 2014) ✅
Ans: BARBARA, CELARENT.
18. Which term is present both in the premises but absent in the conclusion of a syllogism?
Ans: Middle term.
19. How many valid moods are in the third figure?
Ans: Six. (1 Mark, 2013) ✅
20. Which proposition is used as the major premise in all the valid moods of the first figure?
Ans: The first premise of the syllogism.
21. Write the names of the valid moods of the third figure?
Ans: DATISI, DARPATI.
22. What is the position of the middle term in the first figure?
Ans: Subject in the major premise and predicate in the minor premise.
23. State any one valid mood of the third figure? (1 Mark)
Ans: DARAPTI.
24. State any one valid mood of the first figure? (1 Mark)
Ans: CELARENT.
25. How many valid moods are there in the fourth figure?
Ans: Five.
26. How many valid moods are there in the first figure?
Ans: 4 (Four).
27. What will be the conclusion if one of the premises is particular?
Ans: Particular.
28. What will be the conclusion if both the premises of a syllogism are affirmative?
Ans: Affirmative.
29. BOCARDO is a valid mood of which figure?
Ans: Third.
30. How many propositions (premises) are used to construct a syllogism?
Ans: Two.
31. How many terms and propositions are there in a syllogism?
Ans: Three.
Questions and Answers: Mark: 2
1. How many valid moods are there in the second figure of a syllogism?
Ans: Four (4).
2. What do you mean by moods of syllogism? (2 Mark, 2018) ✅
Ans: Mood is the form of a syllogism determined by the quality and quantity of its constituent propositions.
3. What do you mean by the figure of a syllogism? (2 Mark, 2016) ✅
Ans: A figure is the form of the syllogism determined by the position of the middle term in the premises in relation to the major and the minor terms.
4. What is a pure categorical syllogism? (2 Mark)
Ans: It is a form of mediate deductive inference which consists of three categorical propositions and in which the conclusion necessarily follows from the two premises taken together.
5. What do you mean by syllogism? (2 Mark)
Ans: A syllogism is a form of mediate deductive inference in which the conclusion necessarily follows from two premises.
6. Define middle term? (2 Mark)
Ans: Middle term is a term which does not occur in the conclusion but comes in both the premises, and is the common element between them.
7. Define four-term fallacy:
Ans: A syllogism must consist of three terms. If there are more than three terms, it is called the four-term fallacy.
8. Define fallacy of equivocation? (2 Mark)
Ans: A term having more than one meaning is an equivocal term, and such a term used in the syllogism gives rise to the fallacy of equivocation.
9. Define major premise.
Ans: The premise of an inference in which the major term occurs is called the major premise.
10. Define minor premise? (2 Mark)
Ans: The premise of an inference in which the minor term occurs is called the minor premise.
11. Define minor term? (2 Mark)
Ans: The predicate term of the conclusion of a syllogism is called the minor term.
12. What is the fallacy of ambiguity? (2 Mark)
Ans: If a term has more than one meaning, we commit a fallacy called the fallacy of ambiguity.
13. Define fallacy of ambiguous major. (2 Mark)
Ans: If the major term in a syllogism has more than one meaning, then it is called the fallacy of ambiguous major.
14. Define fallacy of ambiguous minor? (2 Mark)
Ans: If the minor term in a syllogism has more than one meaning, then it is called the fallacy of ambiguous minor.
15. Define fallacy of ambiguous middle? (2 Mark)
Ans: If the middle term has more than one meaning in a syllogism, then it leads to a fallacy called the ambiguous middle.
16. What do you mean by undistributed middle? (2 Mark)
Ans: According to a rule of syllogism, the middle term must be distributed at least once in the premises. If this rule is violated, then it is called undistributed middle.
17. Define illicit minor? (2 Mark)
Ans: If the minor term is distributed in the conclusion but remains undistributed in the premise, it is called the fallacy of illicit minor.
18. Define illicit major? (2 Mark)
Ans: If the major term in a syllogism is distributed in the conclusion but remains undistributed in the major premise, then it is called the fallacy of illicit major.
19. State any two valid moods of syllogism of the first figure (2 Mark)
Ans: (i) BARBARA (ii) CELARENT.
20. Mention any two valid moods of the second figure? (2 Mark)
Ans: FESTION, BAROCO.
21. State any two valid moods of the third figure? (2 Mark)
Ans: EFRISON, DARAPTI.
22. State any two valid moods of the fourth figure? (2 Mark)
Ans: FESAPO, DIMARIS.
23. State any two rules of pure categorical syllogism? (2 Mark)
Ans: (i) There must be three propositions in a syllogism. (ii) There are three and only three terms in a syllogism.
24. State any two characteristics of syllogism? (2 Mark)
Ans: (i) Syllogism is a kind of deductive inference, so its conclusion cannot be more general than the premises.
(ii) Syllogism is a mediate deductive inference.
(iii) Its conclusion is drawn from two premises.
25. How many kinds of figures of syllogism? (2 Mark)
Ans: Four kinds.
Question and Answer (4 Marks):
1. Test the validity of the following arguments. (4 Marks)
(a) We are dependent on our cars, Our cars are dependent on drivers. Therefore, we are dependent on drivers.
Ans:
Premise 1: We are those who are dependent on our cars.
Premise 2: Our cars are those who are dependent on drivers.
Conclusion: We are those who are dependent on drivers.
Analysis: The argument is invalid. The premises do not logically lead to the conclusion because there is no direct connection between "we are dependent on cars" and "we are dependent on drivers." The argument fails due to an improper inference.
Verdict: ❌ Invalid.
(b) Only honest persons are happy. John is honest. Therefore, John is happy.
Ans:
Premise 1: All happy people are honest.
Premise 2: John is honest.
Conclusion: John is happy.
Analysis: This argument is an example of a logical fallacy called "affirming the consequent." Just because honesty is necessary for happiness does not mean that all honest people are guaranteed to be happy. This argument ignores other possible factors for happiness.
Verdict: ❌ Invalid (due to undistributed middle term).
2. Test the validity of the following argument. (4 Marks, 2016, 2018)
(a) My arm touches the table, the table touches the floor. Therefore, my arm touches the floor.
Ans:
Premise 1: My arm touches the table.
Premise 2: The table touches the floor.
Conclusion: My arm touches the floor.
Analysis: This argument commits the "four-term fallacy." The premises do not correctly link all the terms to support the conclusion. There is no direct connection between my arm and the floor based on the premises provided.
Verdict: ❌ Invalid (four-term fallacy).
3. Test the validity of the following argument. (4 Marks, 2016)
Argument (a):
All Assamese are intelligent, All Marathis are intelligent. Therefore, all Marathis are Assamese.
Ans:
Premise 1: All Assamese are intelligent (A).
Premise 2: All Marathis are intelligent (A).
Conclusion: Therefore, all Marathis are Assamese (A).
Analysis: This is an example of an "undistributed middle term fallacy."
The term intelligent is used as the middle term in both premises, but it is undistributed in both premises because it's the predicate term in both. An undistributed term is one that does not apply to all members of the class it refers to.
In this case, "intelligent" refers to people from both groups, but it doesn't link the two groups (Assamese and Marathis) in a way that shows they are the same. The argument incorrectly assumes that because both groups are intelligent, they must be the same group.
Verdict: ❌ Invalid (due to undistributed middle term).
4. Test the validity of the following argument. (4 Marks, 2011/2015/2013)
Argument (b):
God created man, man created sin, hence God created sin.
Ans:
Premise 1: Man is that who creates sin (A).
Premise 2: God is that who creates men (A).
Conclusion: Therefore, God is that who creates sin (A).
Analysis: This argument is invalid due to the "four-term fallacy."
The terms involved are:God (who creates men),
Man (who creates sin),
Men (who are created by God),
Sin (created by man).
These four terms do not logically connect in a way that would support the conclusion. The premises don’t establish a valid connection between "God" and "sin." The argument improperly assumes that because God creates men and men create sin, God must therefore create sin.
5. Test the validity of the following argument. (4 Marks, 2011/2018)
Argument (c):
He must be a coward, because he is dishonest and all cowards are dishonest.
Ans:
Premise 1: All cowards are dishonest (A).
Premise 2: He is dishonest (A).
Conclusion: Therefore, he must be a coward (A).
Analysis: This is an example of affirming the consequent, which is a logical fallacy.
While it is true that all cowards are dishonest, it is not necessarily true that all dishonest people are cowards. The premise only establishes that being a coward guarantees dishonesty, but dishonesty does not guarantee cowardice. This is a case where the fallacy of affirming the consequent occurs because the argument assumes that the converse (all dishonest people must be cowards) is true.
6. Test the validity of the following argument. (5 Marks)
Argument (a):
He will pass the examination because he is an intelligent boy and only the intelligent can pass the examination.
Ans:
Premise 1: All who can pass the examinations are intelligent boys (A).
Premise 2: He is an intelligent boy (A).
Conclusion: He is that who will pass the examination (A).
Analysis: This argument is an example of the undistributed middle term fallacy.
The middle term "intelligent boy" is undistributed in both premises. In the first premise, the middle term is in the predicate (not the subject), and in the second premise, it is simply affirmed as a characteristic of the subject. There is no logical connection that allows us to deduce that being an intelligent boy ensures passing the examination.
Verdict: ❌ Invalid (undistributed middle term fallacy).
7. Test the validity of the following argument. (4 Marks)
Argument (b):
He must be happy for he is pious and the pious alone are happy.
Ans:
Premise 1: All happy persons are pious (A).
Premise 2: He is pious (A).
Conclusion: He is happy (A).
Analysis: This argument is another example of the undistributed middle term fallacy.
The middle term "pious" is undistributed in both premises. In premise 1, the middle term is in the predicate, and in premise 2, it is in the subject. The argument assumes that because all happy people are pious, pious people must also be happy, which is not a valid inference. The logical structure does not support the conclusion.
Verdict: ❌ Invalid (undistributed middle term fallacy).
8. Reduce the following syllogistic argument into logical form and test whether it is valid or invalid. (4 Marks, 2018)
Argument (c):
All men are not industrious but he is industrious. So he cannot be a man.
Ans:
Premise 1: Some men are not industrious (D).
Premise 2: He is industrious (A).
Conclusion: He is not a man (E).
Analysis: This argument involves an illicit major term fallacy.
In this syllogism, the major term "man" is distributed in the conclusion but is not distributed in the premises. This leads to an improper conclusion based on a faulty premise structure. The premise that some men are not industrious does not logically support the conclusion that the industrious person cannot be a man. The argument fails because the distribution of terms is incorrect.
Verdict: ❌ Invalid (illicit major term fallacy).
9. Define syllogism. State three general rules of categorical syllogism. (4 Marks)
Ans:
Syllogism is a form of reasoning in which a conclusion is drawn from two related premises. It is a mediate deductive inference, meaning the conclusion is reached by connecting the premises through a middle term.
Example:Premise 1: All men are mortal.
Premise 2: All kings are men.
Conclusion: Therefore, all kings are mortal.
Three general rules of categorical syllogism:
Three members of proposition: There must be three components in a syllogism—two premises and one conclusion.
Three terms in the syllogism: A syllogism must involve exactly three distinct terms—the major term, minor term, and middle term.
Middle term distribution: The middle term must be distributed at least once in the premises. This is necessary for valid inference between the major and minor terms.
Affirmative premises: If one of the premises is negative, the syllogism cannot provide a valid conclusion. At least one premise must be affirmative.
No conclusion from two particular premises: If both premises are particular (using terms like "some"), no valid conclusion can be drawn.
10. State four characteristics of categorical syllogism. (4 Marks, 2015)
Ans:
Three propositions: A categorical syllogism consists of three propositions—two premises and one conclusion.
Three terms: There are exactly three distinct terms in a syllogism: major term, minor term, and middle term.
Deductive inference: Syllogism is a deductive form of reasoning, meaning the conclusion necessarily follows from the premises.
Concerned with formal truth: A syllogism is concerned with the formal correctness of the logical structure rather than the actual truth of the premises.
Conclusion limitation: The conclusion of a syllogism cannot be more general than the two premises. The logical structure requires the conclusion to be a necessary result of the premises.
11. What do you mean by the figure of syllogism? How many types of figures of syllogism are there? Discuss. (4 Marks, 2014)
Ans:
Figure of syllogism refers to the arrangement or position of the middle term in the two premises of a syllogism in relation to the major and minor terms. The figure determines how the middle term is used to establish the connection between the major and minor terms.
There are four figures of syllogism, which are categorized based on the positions of the middle term:
First Figure:
Form:
Major Premise: M - P (Middle term - Major term)
Minor Premise: S - M (Minor term - Middle term)
Conclusion: S - P (Minor term - Major term)
Example:
Major Premise: All men are mortal.
Minor Premise: Socrates is a man.
Conclusion: Socrates is mortal.
Second Figure:
Form:
Major Premise: P - M
Minor Premise: S - M
Conclusion: S - P
Example:
Major Premise: No humans are immortal.
Minor Premise: All men are humans.
Conclusion: No men are immortal.
Third Figure:
Form:
Major Premise: M - P
Minor Premise: M - S
Conclusion: S - P
Example:
Major Premise: All birds can fly.
Minor Premise: All sparrows are birds.
Conclusion: All sparrows can fly.
Fourth Figure:
Form:
Major Premise: P - M
Minor Premise: M - S
Conclusion: S - P
Example:
Major Premise: All fish are aquatic.
Minor Premise: All salmon are fish.
Conclusion: All salmon are aquatic.
Each figure has a specific logical structure that impacts how valid conclusions can be drawn based on the premises.
12. Define syllogism and provide an example. (4 Marks, 2012)
Ans: A syllogism is a form of reasoning where a conclusion is drawn from two premises. The conclusion necessarily follows from the premises, and this form of reasoning is known as mediate deductive inference.
Example:
Premise 1: All men are mortal.
Premise 2: All kings are men.
Conclusion: All kings are mortal.
This example illustrates a valid syllogism where the conclusion follows directly from the two premises.
13. State the definition of pure categorical syllogism with an example. (4 Marks)
Ans: A pure categorical syllogism is a type of mediate deductive inference where a conclusion is drawn from two categorical premises. All the propositions in this type of syllogism are categorical, meaning they assert or deny something about a subject.
Example:
Premise 1: All men are mortal (A).
Premise 2: All poets are men (A).
Conclusion: All poets are mortal (A).
In this example, the conclusion follows logically from the two categorical premises, and this forms a pure categorical syllogism.
14. What do you mean by the figure of syllogism? What is the position of the middle term in the first figure? (4 Marks)
Ans: The figure of syllogism refers to the arrangement of the middle term in the premises of a syllogism. The placement of the middle term affects how the conclusion is drawn and determines the figure of the syllogism.
In the first figure, the middle term is placed:
As the subject in the major premise.
As the predicate in the minor premise.
This arrangement ensures that the conclusion can validly follow from the premises.
15. What is the mood of a syllogism? How many kinds of valid moods are there in syllogism? Mention them. (1 Mark)
Ans: The mood of a syllogism refers to the form of the syllogism, determined by the type of propositions (A, E, I, O) used in the premises and the conclusion. The letters A, E, I, and O represent the four types of categorical propositions:
A: Universal Affirmative ("All A are B")
E: Universal Negative ("No A are B")
I: Particular Affirmative ("Some A are B")
O: Particular Negative ("Some A are not B")
There are four valid moods in syllogism, commonly denoted by combinations of A, E, I, and O:
AAA - Universal affirmative in both premises and the conclusion.
EAE - Universal negative in the major premise, universal affirmative in the minor premise, and negative conclusion.
AII - Universal affirmative in the major premise, particular affirmative in the minor premise, and particular affirmative conclusion.
OAO - Particular negative in both premises and the conclusion.
These valid moods are used to form valid syllogisms and ensure correct logical reasoning.
16. What is the function of the middle term in a syllogism? (4 Marks, 2013, 2014, 2015)
Ans: The middle term in a syllogism serves a critical role in establishing the logical connection between the minor term (the subject of the conclusion) and the major term (the predicate of the conclusion). The function of the middle term can be outlined as follows:
Middle term links the premises: It serves as a bridge between the major and minor terms, creating the relationship that leads to the conclusion.
Absent in the conclusion: The middle term does not appear in the conclusion of a syllogism. It only appears in the two premises, facilitating the logical connection.
Must be distributed once: For the syllogism to be valid, the middle term must be distributed at least once in the premises, meaning it must refer to all members of the category it represents in one of the premises.
Establishes relation: The middle term is essential in establishing the necessary relation between the major and minor terms, ensuring that the conclusion follows from the premises.
In summary, the middle term is central to creating the logical structure in a syllogism, even though it does not appear in the conclusion.
17. Prove that in the Second Figure, one of the premises must be negative. (4 Marks, 2011)
Ans: In the Second Figure of syllogism, the middle term occupies the predicate position in both the major and minor premises. The structure of a syllogism in the Second Figure is as follows:
Major Premise: P - M (Middle term is the predicate of the major premise)
Minor Premise: S - M (Middle term is the predicate of the minor premise)
Conclusion: S - P (Minor term is the subject, and the major term is the predicate)
For the syllogism in the second figure to be valid, one of the premises must be negative. This is because:
In this figure, the middle term is the predicate in both premises. For the premises to provide a valid logical connection to the conclusion, one of the premises must be negative to prevent the middle term from being inappropriately linked to both the subject and predicate in the conclusion.
A negative premise ensures that there is a logical separation between the subject and predicate, allowing the conclusion to be drawn correctly.
In conclusion, in the second figure, having at least one negative premise is necessary to prevent logical fallacies and ensure that the conclusion is valid.
Questions and Answers: Mark : 5
1. State five general rules of pure categorical syllogism. (5 Marks, 2012)
Ans:
Three propositions: There are three propositions in a pure categorical syllogism—two premises and one conclusion.
Three terms: A pure categorical syllogism must involve three distinct terms—the major term, minor term, and middle term.
Middle term distribution: The middle term must be distributed at least once in the premises, as it is necessary to establish a valid relationship between the major and minor terms.
One conclusion: A valid syllogism can only produce one conclusion that logically follows from the premises. The conclusion must not be more general than the premises.
At least one affirmative premise: If both premises are negative, the syllogism is invalid. At least one of the premises must be affirmative to yield a valid conclusion.
These general rules help ensure that a pure categorical syllogism is logically sound and valid.
2. What do you mean by the figure of syllogism? How many types of figures of syllogism? Discuss. (5 Marks)
Ans:
A figure of syllogism refers to the form of a syllogism, which is determined by the position of the middle term in the premises in relation to the major and minor terms. The position of the middle term influences the logical structure and determines the figure of the syllogism. There are four types of figures in syllogism:
First Figure:
In this figure, the middle term is the subject in the major premise and the predicate in the minor premise.
Example:
Major Premise: M - P (Middle term is the subject)
Minor Premise: S - M (Middle term is the predicate)
Conclusion: S - P (The conclusion connects the minor and major terms)
Second Figure:
In this figure, the middle term is the predicate in both premises.
Example:
Major Premise: P - M (Middle term is the predicate)
Minor Premise: S - M (Middle term is the predicate)
Conclusion: S - P (The conclusion connects the minor and major terms)
Third Figure:
In this figure, the middle term is the subject in both premises.
Example:
Major Premise: M - P (Middle term is the subject)
Minor Premise: M - S (Middle term is the subject)
Conclusion: S - P (The conclusion connects the minor and major terms)
Fourth Figure:
In this figure, the middle term is the predicate in the major premise and the subject in the minor premise.
Example:
Major Premise: M - P (Middle term is the predicate)
Minor Premise: M - S (Middle term is the subject)
Conclusion: S - P (The conclusion connects the minor and major terms)
Each of these figures provides a different way in which the middle term is positioned within the premises, which ultimately affects the logical flow and validity of the syllogism.
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