UGC NET Questions (Paper – 1)

Statements A, B, C and E correctly characterise the biconditional connective. A and C together state that p ↔ q is true when p and q match in truth value and false otherwise. B is correct since p ↔ q decomposes into (p → q) and (q → p). E is true because swapping p and q in a biconditional does not change its meaning. D is false; with two propositional variables, the truth table has four rows, and the biconditional is true in exactly two of them (both true or both false), not three. Therefore, A, B, C and E only form the correct set.

Option A:
Option A is correct because it collects all four accurate properties and excludes D, which miscounts the true rows of the biconditional. It matches the logical behaviour of “if and only if” as tested in NET reasoning.

Option B:
Option B is incomplete as it leaves out E, so it does not mention the commutative nature of the connective, even though that is an important structural property. Without E, the description is not fully comprehensive.

Option C:
Option C is incorrect because, while B and C and E are true, it omits A, which directly states the key condition about matching truth values. The option therefore does not explicitly identify the central truth condition of the biconditional.

Option D:
Option D is wrong because it retains D, the statement that there are three true rows, which is factually incorrect, and it omits B. Once a wrong statement is included, the option cannot represent the exact set of correct statements.

Statements D and E are wrong, while A, B, C and F are correct. A and B correctly describe the truth conditions for conjunction and inclusive disjunction, and C accurately symbolises the exclusive “either–or”. F is true because truth tables are standard tools for checking validity. D mistakenly describes a tautology instead of a contradiction, and E wrongly describes the condition for a contingent statement rather than a tautology, so these two are the wrong statements.

Option A:
Option A is incorrect because it singles out only D as wrong and ignores E, which also misrepresents the definition of a tautology. Since both D and E give inverted definitions, treating only one of them as wrong undercounts the errors. Therefore this option does not match the full set of wrong statements.

Option B:
Option B is also incomplete, as it selects only E and ignores D. D is clearly false because a contradiction is never true in any assignment, not always true. By failing to include D, this option again fails to capture all wrong statements listed.

Option C:
Option C is correct because it groups exactly D and E, the two statements that invert the standard meanings of contradiction and tautology. It leaves A, B, C and F untouched, all of which correctly describe truth-functional connectives and the use of truth tables. This combination therefore matches the required set of wrong statements.

Option D:
Option D is wrong because it adds B, which is a correct description of inclusive disjunction, to the set of wrong statements. B rightly states that “p or q” is false only when both p and q are false. Including B beside the genuinely wrong D and E makes the option logically inconsistent.

Two propositions are logically equivalent when they share the same truth value in all possible circumstances. A joint truth table reveals this by showing matching columns for the two statements on every row. Logical equivalence means that each proposition implies the other, so they stand or fall together. Accordingly, the relationship described in the stem is that of logical equivalence.

Option A:
Option A is correct because logical equivalence formalises the idea of identical truth behaviour across all valuations. This relation can also be expressed using a biconditional, reflecting mutual implication. The truth-table condition in the question is the standard test for such equivalence.

Option B:
Option B, contradictory, would require that one proposition be true whenever the other is false and vice versa. This implies opposite truth values on every row, not identical ones. Therefore contradiction is not what the stem describes.

Option C:
Option C, inconsistent, typically refers to a set of propositions that cannot all be true together. It does not describe a relation between two single propositions having matching truth values under all conditions. Hence inconsistent is not appropriate here.

Option D:
Option D, independent, suggests that the truth of one proposition has no fixed effect on the truth of the other, so their truth values are not reliably correlated. This is the opposite situation to having identical truth values on every row.

Conjunction is the compound statement formed by connecting two propositions with "and". According to its truth table, a conjunction is true only when each conjunct is true. This aligns with our intuitive understanding that both conditions must be met. Therefore the connective described in the question is correctly termed conjunction.

Option A:
Option A is correct because conjunction specifically denotes the logical operator that joins statements with "and" and demands the truth of all of them. It is one of the fundamental truth-functional connectives in propositional logic. The stem’s description matches this behaviour exactly.

Option B:
Option B, disjunction, connects statements with "or" and is usually interpreted in logic as true if at least one of the disjuncts is true. It does not require both components to be true, so it does not fit the question.

Option C:
Option C, implication, represents a conditional statement of the form "if p, then q". Its truth conditions differ significantly from those of conjunction and do not match the requirement that both parts be true.

Option D:
Option D, negation, operates on a single proposition by reversing its truth value. It does not combine two statements at all and thus cannot be the connective described.

Disjunction is the logical operation that forms a compound statement using "or". In its inclusive sense used in standard logic, a disjunction is true when at least one of the disjuncts is true and false only when both are false. This behaviour corresponds exactly to the description in the stem. Hence the connective is called disjunction.

Option A:
Option A, conjunction, links statements with "and" and is true only when both conjuncts are true. Its falsity conditions are therefore quite different and do not match the pattern described. Thus conjunction is not the correct answer.

Option B:
Option B is correct because disjunction accurately characterises the truth conditions stated: it fails only when neither component is true. This makes disjunction the appropriate technical term for the "or" connective in propositional logic.

Option C:
Option C, biconditional, expresses "p if and only if q" and is true when both components share the same truth value. This is more restrictive than the simple "or" relation and does not correspond to the stem.

Option D:
Option D, negation, alters the truth value of a single statement and does not combine two statements with "or". Consequently negation cannot be the intended connective.

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.

A tautology is a compound proposition that evaluates to true under every possible assignment of truth values to its component propositions. It is logically true by virtue of its form rather than specific factual content. In a full truth table, the column for a tautology’s final result contains only Ts and no Fs. Because of this feature, tautologies play an important role in testing argument forms and deriving equivalences.

Option A:
Option A matches the formal definition of a tautology as a statement that never turns out false in any row of its truth table. It captures the idea of logical necessity independent of empirical facts.

Option B:
Option B describes a contradiction, which is always false and has only Fs in its truth table, the exact opposite of a tautology.

Option C:
Option C refers to a contingency, which is true on some valuations and false on others, so it is neither tautological nor contradictory.

Option D:
Option D suggests that the statement cannot be tested, which is incorrect because tautologies are routinely checked using truth tables and formal methods.

A contradiction is a statement that cannot be true in any possible situation because its form guarantees falsity on every line of its truth table. It is logically inconsistent and unsatisfiable, meaning no assignment of truth values makes it hold. Such statements often arise from combining a claim and its negation. Therefore the statement described in the stem is accurately called a contradiction.

Option A:
Option A is correct because contradictions exhibit the extreme case of logical falsity: they are false in all possible worlds or under all valuations. Recognising contradictions is important in proofs by contradiction and in detecting inconsistent sets of premises.

Option B:
Option B, tautology, is the exact opposite: a statement that is true under every possible assignment of truth values. While it also has a uniform truth-value pattern, that pattern is truth rather than falsehood.

Option C:
Option C, contingency, is true under some assignments and false under others, which is the normal status of most factual claims. The stem, however, speaks of a statement that is false in every possible case.

Option D:
Option D, hypothesis, refers to a provisional assumption or conjecture and does not specify a particular truth-table pattern. A hypothesis could be a tautology, contradiction or contingency depending on its logical form and content.

A contingency is a statement whose truth value varies across different possible assignments of truth values to its components. It is neither always true nor always false. Most ordinary factual statements have this contingent status. Therefore the description in the stem refers to a contingency.

Option A:
Option A is correct because contingency is the standard name for propositions that can be true in some circumstances and false in others. This intermediate status contrasts with tautologies and contradictions and matches the mixed truth behaviour described.

Option B:
Option B, tautology, is true under every valuation and so lacks the possibility of being false. This does not match the stem’s indication that the statement is sometimes false. Hence tautology is not suitable.

Option C:
Option C, contradiction, is false under every valuation and therefore is never true. The question, however, specifies that the statement is sometimes true, so contradiction cannot be the answer.

Option D:
Option D, theorem, is a result that has been proved within a logical or mathematical system and may or may not be tautological depending on the system. It is not defined by having mixed truth values. Thus theorem is not the best term here.

Statements A, B and C give the standard truth conditions for conjunction, inclusive disjunction and negation in classical logic. Statement E is also correct because truth tables are precisely the tool used to define and study these connectives. Statement D is false, since a conjunction requires both conjuncts true and not just one. Thus the full set of correct statements is A, B, C and E only, which matches option B.

Option A:
Option A is incorrect because it omits E, even though using truth tables to define connectives is a central logical technique. It therefore lists only part of the true information and does not capture the complete correct set.

Option B:
Option B is correct since it includes all and only the true statements: the right truth conditions for ∧, ∨ and ¬ together with the role of truth tables in defining them, while excluding D, which misstates when a conjunction is true.

Option C:
Option C is wrong because it includes D, the false claim that a conjunction is true if at least one conjunct is true, and it omits B, so it both accepts an incorrect statement and fails to include a correct one.

Option D:
Option D is incorrect because although B, C and E are true, it drops A, which gives the fundamental condition for conjunction, so it does not contain the entire set of correct statements for this question.