UGC NET Questions (Paper – 1)

Statements A, B, C and D correctly relate “if”, “only if” and necessary conditions to their symbolic forms, and F is also true, while E is false. The biconditional is true exactly when p and q share the same truth value, not when they differ. Treating “only if” carefully is crucial for distinguishing what is necessary from what is sufficient. Hence the correct set of statements is A, B, C, D and F only.

Option A:
Option A is incomplete because it omits D and F, leaving out both the explicit link to necessary conditions and the exam relevance of misreading “only if”. Although A, B, C and E mention some relationships, they include E, which wrongly states the truth pattern of the biconditional. This makes the option incorrect.

Option B:
Option B is wrong because it includes E, which claims that “p if and only if q” is true when p and q differ in truth value. That is the truth condition for exclusive disjunction, not for the biconditional. Including E makes the combination logically inconsistent.

Option C:
Option C is correct as it gathers A, B, C and D, which correctly express equivalences and necessary condition symbolism, and F, which notes the importance of reading these connectives properly in exams. It excludes E, avoiding the confusion between biconditional and exclusive or. This matches standard logical teaching.

Option D:
Option D is incorrect since it omits A and replaces it with B, C, D, E and F. Without A, the equivalence of “p only if q” with “If p then q” is not stated, and including E still misrepresents the truth conditions of the biconditional. Therefore it cannot be the right answer.

The contrapositive of a conditional "if p, then q" is formed by negating both the antecedent and the consequent and reversing their positions, giving "if not q, then not p". In classical logic, a conditional and its contrapositive are always logically equivalent. This means they share the same truth table and stand or fall together. Hence the statement described is called the contrapositive.

Option A:
Option A, converse, yields "if q, then p" by swapping the antecedent and consequent without negating them. The converse is not necessarily equivalent to the original and thus does not match the pattern in the question.

Option B:
Option B, inverse, gives "if not p, then not q" by negating both parts but keeping their positions. Like the converse, the inverse is not generally equivalent to the original conditional. Therefore inverse is not the correct answer.

Option C:
Option C, biconditional, expresses "p if and only if q" and asserts both directions of implication in one statement. It is a different connective altogether and not merely a transformation of a single conditional.

Option D:
Option D is correct because contrapositive is the recognised name for the transformed conditional that is always logically equivalent to the original. This equivalence underlies many proof techniques.

Statement B gives the correct falsity condition for inclusive disjunction: it fails only when both components are false. C and D are De Morgan’s laws for negation of conjunction and disjunction, both of which are valid equivalences in classical logic. A is false; a conjunction requires both p and q to be true, not just at least one. E is false because in two-valued logic, a statement and its negation cannot be true together. Therefore B, C and D only are correct.

Option A:
Option A is incomplete as it omits D and so does not state the second De Morgan equivalence, leaving the treatment of negation of disjunction unfinished.

Option B:
Option B is incorrect because it includes E, which claims that a statement and its negation can both be true, contradicting the law of non-contradiction in classical logic.

Option C:
Option C is wrong since it accepts A, which incorrectly describes the truth condition for conjunction, and therefore introduces a clear error into the combination.

Option D:
Option D is correct as it gathers the proper truth condition for disjunction and both De Morgan laws, while excluding A and E, which misrepresent conjunction and the mutual exclusivity of a statement and its negation.

Contraries are propositions that cannot both be true at the same time but can both be false. On the square of opposition, the universal affirmative 'All S are P' and the universal negative 'No S are P' have this relation. There are circumstances where neither statement holds, making both false. Thus the relationship described in the stem is that of contraries.

Option A:
Option A, contradictories, are pairs of propositions that cannot both be true and cannot both be false; exactly one must be true. This relation holds between A and O or E and I, not between A and E. Therefore contradictories is not correct here.

Option B:
Option B, subcontraries, are propositions that cannot both be false but can both be true, a relation found between I and O propositions. Universal statements do not stand in this relation, so subcontraries cannot be the right answer.

Option C:
Option C, subalterns, refers to pairs where the truth of a universal implies the truth of its corresponding particular, such as A implying I. This is a different relation from the one asked about in the question.

Option D:
Option D is correct because contraries specifically describe the relation between universal affirmative and universal negative propositions on the square of opposition, matching the description in the stem.

Statements A, B, C and E correctly state the truth conditions and logical role of biconditionals, while D is false. “If and only if” requires that p and q share the same truth value, which can be expressed as two conditionals taken together. It is false exactly when one is true and the other false. Far from being only sufficient, p is both necessary and sufficient for q in a biconditional, so D misdescribes the relation. Recognising this helps with equivalence transformations in UGC NET questions.

Option A:
Option A is incomplete because it omits E, not mentioning how biconditionals feature in exam-style equivalence problems. A, B, C only therefore leaves out a key application of the concept.

Option B:
Option B is wrong since it drops A, thereby failing to state in general that biconditionals are true when p and q match in truth value. B, C, E only provides specific and exam-related facts but lacks the core truth-condition statement.

Option C:
Option C is correct as it gathers all the true statements and excludes D, which restricts the relation to sufficiency alone. This option aligns with standard propositional logic and how biconditionals are tested in symbolic reasoning questions.

Option D:
Option D is incorrect because it omits B, losing the important equivalence of a biconditional with two conditionals. A, C, E only is therefore not acceptable as the right answer.

Statements A, B and C are all correct. A notes the common natural-language use of “either” as exclusive. B is true because the standard logical disjunction is inclusive and allows both A and B to be true. C correctly gives a formula for exclusive-or using OR, AND and NOT. D is false since exam questions may clarify whether the sense is inclusive or exclusive, and E is false because inclusive and exclusive or differ when both A and B are true. Hence, A, B and C only are correct.

Option A:
Option A is incomplete since it omits C, thereby failing to mention the formal definition of exclusive-or in terms of other connectives, which is important in logical reasoning.

Option B:
Option B is incorrect because it incorrectly includes D, which claims that exam usage is always exclusive, and so introduces a false constraint on interpretation.

Option C:
Option C is correct as it combines natural-language usage, the inclusive logical meaning and the formal construction of exclusive-or, while excluding D and E, which misstate exam conventions and truth-value patterns.

Option D:
Option D is wrong since it includes E, which wrongly claims that inclusive and exclusive or always agree, and it drops A, losing the important point about everyday interpretation.

The phrase “either P or Q, but not both” specifies exclusive disjunction. This means at least one of P or Q is true, and they are not simultaneously true. Symbolically, we combine the inclusive disjunction P ∨ Q with the negation of their conjunction, ¬(P ∧ Q). The conjunction of these two conditions, (P ∨ Q) ∧ ¬(P ∧ Q), precisely encodes exclusivity.

Option A:
Option A, P ∨ Q, is inclusive “or” and allows the possibility that both P and Q are true, which is not allowed in the exclusive reading.

Option B:
Option B adds the restriction that P and Q cannot both hold, yielding the desired “one but not both” condition.

Option C:
Option C, P ∧ Q, demands that both P and Q are true together, the opposite of what exclusivity requires.

Option D:
Option D expresses logical equivalence or biconditional, requiring P and Q to share the same truth value, which is different from exclusive disjunction.

A truth functional connective is defined by the way it systematically turns combinations of truth values of component statements into a truth value for the whole. For such connectives, once the truth values of the parts are known, the truth of the compound is completely determined. Examples include conjunction, disjunction, conditional and biconditional as studied in truth tables. Thus the connective described in the stem is properly called truth functional.

Option A:
Option A, intensional, usually refers to expressions whose meaning involves more than just extension or truth value, such as belief operators, and so is not restricted to connectives determined purely by truth values. Intensional contexts often break straightforward truth-functionality. Therefore intensional is not the correct label here.

Option B:
Option B is correct because truth functional connectives behave exactly as the stem describes: their semantic contribution can be fully represented in a truth table. This makes them central to classical propositional logic.

Option C:
Option C, non truth functional, would describe connectives or operators whose effect cannot be captured solely by reference to the truth values of component statements, which is the opposite of what the question states.

Option D:
Option D, analogical, has to do with reasoning by analogy between cases rather than with how connectives determine truth values. It is unrelated to the technical notion of truth-functionality.

Statements A, B and C describe standard facts about implication. A gives the important equivalence p → q ≡ ¬p ∨ q. B correctly states that an implication is false only when the antecedent is true and the consequent false. C correctly identifies the contrapositive as ¬q → ¬p. D is false because ¬p → ¬q is the inverse, not the converse, and E is false since p → q is generally not equivalent to q → p. Therefore A, B and C only are correct.

Option A:
Option A is incomplete because it omits C and thus fails to mention the contrapositive, which is central to reasoning with implications in many NET questions.

Option B:
Option B is incorrect as it includes D, which mislabels the inverse as the converse and therefore misuses terminology in logic.

Option C:
Option C is wrong because it omits A and therefore drops a key equivalence used to simplify implications.

Option D:
Option D is correct since it combines the truth-table characterisation of implication, the disjunctive form and the contrapositive, while excluding D and E, which contain conceptual errors about converse and equivalence.

Syādvāda implements anekāntavāda in language by prefacing statements with “syāt” (from a certain standpoint) and expanding them into seven possible forms. These combine affirmation, negation and indescribability under specific conditions. The scheme allows Jains to express how a claim can be true in some respects and false in others. It thus provides a logical tool for handling many sided reality in discourse.

Option A:
Option A contradicts the Jain project, because syādvāda complicates simple two valued logic rather than enforcing it.

Option B:
Option B correctly describes syādvāda as a sevenfold conditional mode of predication using “syāt” to mark standpoint dependence.

Option C:
Option C reduces the doctrine to ritual, ignoring its conceptual and logical content in Jain philosophy.

Option D:
Option D is too sceptical; Jains hold that language can express qualified truths when properly framed by standpoints.

A is correct because logical equivalence is defined via matching truth values in all cases. B is true as p → q is truth-functionally the same as ¬p ∨ q. D is correct since a conditional and its contrapositive always share the same truth table. C is wrong because p → q and q → p are converses and need not share truth values, and E is wrong since equivalence is about truth conditions, not syntactic identity. Therefore, C and E only are the wrong statements.

Option A:
Option A is correct because it identifies exactly C and E as the problematic statements, leaving intact the proper definitions and equivalences in A, B and D. It aligns with standard logical theory taught for NET.

Option B:
Option B considers only C as wrong and mistakenly treats E as acceptable, despite E conflating syntactic form with semantic equivalence. It therefore misses one incorrect statement.

Option C:
Option C treats only E as wrong and ignores the clear counterexamples to C where p → q and q → p differ, so it does not cover all wrong statements.

Option D:
Option D includes D among wrong statements, even though D is correct about contrapositive equivalence, and so misclassifies a true principle along with the false ones.

Statements A, B, C, D and E correctly characterise material implication and the distinction between necessary and sufficient conditions, while F is false. “If p then q” is indeed false only when p is true and q is false, and necessary conditions are those without which an outcome cannot obtain. Sufficient conditions guarantee an outcome when they occur, and confusing the two leads to errors like affirming the consequent. In the rain example, rain is treated as sufficient for wet ground, though not necessary because there may be other causes. Statement F reverses the relation between square and rectangle, since being a square is sufficient but not necessary for being a rectangle. Hence A, B, C, D and E only is the correct combination.

Option A:
Option A is correct because it includes all five accurate statements and excludes F, which mislabels the necessity relation between square and rectangle. It reflects standard logical semantics and familiar examples used in reasoning questions. Thus this option represents the complete and correct set of statements.

Option B:
Option B is incorrect since it adds F to the otherwise correct set, thereby endorsing a false description of the relationship between squares and rectangles. Squares meet the definition of rectangles, so being a rectangle is necessary for being a square, not the other way round. Including F therefore makes this option unsound.

Option C:
Option C is wrong because it omits B, leaving out the explicit definition of a necessary condition. Without B, the account of conditionals and conditions is incomplete, even though A, C, D and E are true. Therefore A, C, D and E only cannot be chosen.

Option D:
Option D is incorrect because it leaves out A and includes F, thereby ignoring the truth condition of material implication and accepting a mistaken example. This combination does not accurately represent the full set of correct statements about conditionals.

A set of statements is inconsistent if they cannot all be true at the same time. Saying “Some teachers are strict” asserts the existence of at least one strict teacher. Saying “No teacher is strict” denies that any teacher is strict. These two claims cannot both be true together; if one is true, the other must be false. Hence, this pair is logically inconsistent.

Option A:
Option A’s two statements are compatible, because if all poets are imaginative, then certainly some poets are imaginative, so both can be true together.

Option B:
Option B directly pits an existential claim against a universal negative about the same property, creating a clear contradiction.

Option C:
Option C is consistent because if all birds can fly and penguins are birds, it follows that penguins can fly within that system, even if this conflicts with real world facts.

Option D:
Option D is also consistent, allowing for a mixed group of scientists, some honest and some not, which poses no logical problem.