UGC NET Questions (Paper – 1)

Negation in propositional logic is often represented by the symbol ¬ placed before a proposition. It expresses the logical opposite of the statement’s truth value: if the original proposition is true, its negation is false, and vice versa. This operator is fundamental in constructing complex statements and in defining other connectives using truth tables.

Option A:
Option A, ¬, is the standard modern symbol for “not,” used widely in logic texts and formal reasoning. It unambiguously marks the negation of whatever proposition follows it.

Option B:
Option B, ∧, denotes conjunction and is used for “and,” not for negation.

Option C:
Option C, ∨, is the symbol for disjunction, corresponding to “or,” and has a different truth function.

Option D:
Option D, ↔, stands for biconditional, “if and only if,” which expresses equivalence rather than negation.

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.