UGC NET Questions (Paper – 1)

A hypothetical syllogism links conditionals in a chain, using the fact that if P leads to Q and Q leads to R, then P must lead to R. This is a transitive property of the conditional relation and is a recognised valid inference form. It essentially passes the implication through the intermediate step Q.

Option A:
Option A clearly shows the chain P → Q and Q → R leading to P → R, which is valid in standard propositional logic.

Option B:
Option B does not guarantee any relation between P and R; both lead to Q, but nothing links P to R or vice versa.

Option C:
Option C reverses the conclusion and improperly suggests that R implies P, which does not follow from the premises.

Option D:
Option D asserts Q → R, but from P → Q and P → R we cannot generally infer that Q implies R, because Q could arise from other causes without R.

To say that p is necessary for q means that q cannot be true unless p is true. This is equivalent to saying that if p is absent, q must also be absent. Formally, this is symbolised as "if not p, then not q". Thus the conditional described in Option B captures the idea of necessity.

Option A:
Option A, "if p,then q", expresses that p is sufficient for q, since whenever p occurs, q follows. While related, sufficiency and necessity are different relations, and this conditional does not directly state that p is required for q.

Option B:
Option B is correct because "if not p,then not q" asserts that the failure of p guarantees the failure of q, which is exactly what a necessary condition demands. It is logically equivalent to the natural-language statement about necessity.

Option C:
Option C, "if q,then not p", says that whenever q is true, p must be false. This is the opposite of a necessity claim (which requires p when q holds) and would make p incompatible with q rather than required for it. Therefore it cannot represent "p is necessary for q".

Option D:
Option D, "if not q,then p", suggests that the absence of q guarantees the presence of p, a relation unrelated to standard necessity formulation. It neither captures necessity nor sufficiency as usually defined and so cannot be correct.

A sufficient condition is one whose presence guarantees that a certain event or property will occur, even though the event might also arise in other ways. If the sufficient condition holds, the specified outcome must follow. This notion is central in both logic and causal reasoning where we want to know what factors are enough to bring about a result. Hence the condition described in the stem is a sufficient condition.

Option A:
Option A, necessary, refers to a condition that must be present for an event to occur but may not be enough on its own to produce it. Necessity emphasises requirement, not guarantee, and so does not match the wording in the question.

Option B:
Option B is correct because sufficiency highlights that the condition is adequate on its own to secure the event. For example, being a square is sufficient for being a rectangle, since every square is automatically a rectangle. This captures the sense of “enough by itself” mentioned in the stem.

Option C:
Option C, accidental, suggests that a factor accompanies an event by chance and does not reliably bring it about. Accidental conditions fail to meet the requirement of guaranteeing the outcome.

Option D:
Option D, remote, implies distance or weak relevance and is not a standard logical term for describing the relation between conditions and events. It does not indicate any guarantee of occurrence.

A sufficient condition is one whose presence ensures that a specified event will occur. Whenever the sufficient condition holds, the event must follow. However, the event might also occur due to different sufficient conditions. Thus the description of a guarantee in the stem accurately captures the idea of a sufficient condition.

Option A:
Option A, incidental, suggests something that occurs by chance or as a side effect. Incidental factors do not reliably guarantee outcomes. Therefore incidental is not the logical term indicated by the question.

Option B:
Option B, necessary, refers to a condition that must be present but may not by itself produce the event. Necessary conditions do not guarantee occurrence when considered alone. Hence necessary is not the correct answer here.

Option C:
Option C correctly identifies sufficient as the type of condition whose presence is enough to ensure the event. This concept is central to understanding causal and logical relationships. Therefore sufficient condition is the best match for the stem.

Option D:
Option D, remote, implies distance or weak connection and has no precise meaning in standard conditional analysis. A remote factor need not guarantee an outcome. Consequently remote is not suitable as an answer.

Modus tollens is a valid form of argument that denies the antecedent by denying the consequent of a conditional. It proceeds from “if p, then q” and “not q” to the conclusion “not p”. This preserves truth because if p were true, q could not be false. Therefore the pattern described in the stem is known as modus tollens.

Option A:
Option A, affirming the consequent, argues from “if p then q” and “q” to “p”. This pattern is invalid because q might be true for other reasons. Thus affirming the consequent is a fallacy, not the valid form in the question.

Option B:
Option B correctly names modus tollens as the rule that infers “not p” from “if p then q” and “not q”. It is a central tool in deductive proof and refutation. Hence this option accurately answers the question.

Option C:
Option C, denying the antecedent, moves from “if p then q” and “not p” to “not q”. This is also invalid because q could still be true for other causes. Therefore denying the antecedent cannot be the form intended by the stem.

Option D:
Option D, reductio error, is not a standard label for this precise conditional pattern. While reductio arguments sometimes use similar ideas, the technical name of the form in the question is modus tollens.

The pattern "if p, then q; not p; therefore not q" is invalid because q may still be true even if p is false. This error is known as the fallacy of denying the antecedent. It mistakenly treats the conditional as though p were a necessary condition for q, which the original statement does not assert. Therefore the fallacy described is denying the antecedent.

Option A:
Option A, affirming, corresponds to affirming the consequent, a different fallacy with the form "if p, then q; q; therefore p". It does not match the structure that begins with "not p". Hence affirming is not correct here.

Option B:
Option B is correct because the erroneous step is to deny the antecedent p and then incorrectly deny the consequent q, assuming q depends exclusively on p. This misinterpretation of the conditional leads to an invalid inference.

Option C:
Option C, strengthening, is not a standard label for any recognised formal fallacy in this context and does not capture the problem of negating p. It therefore cannot be the answer.

Option D:
Option D, converting, might suggest swapping antecedent and consequent, but the structure in the stem is not about such reversal; it is about drawing an unwarranted negative conclusion from the denial of p. Thus converting is inappropriate.