Logical connectives and implication – UGC NET Question

Statement C is wrong because in standard truth-functional logic the conditional “if p then q” is false precisely when p is true and q is false, not when p is false and q is true. Statements A and B correctly describe the conditions for truth of conjunction and inclusive disjunction, while D accurately explains the biconditional and E states the essential idea that compound truth values depend on component truth values. Hence, C alone is the incorrect statement, so the option that lists only C is correct.

Option A:
Option A is correct since it identifies C as the sole misstatement and implicitly accepts A, B, D and E as standard truth-table definitions. It preserves the conventional semantics of implication while rejecting the inverted condition given in C.

Option B:
Option B is incorrect because it also labels A as wrong, even though A correctly states that “p and q” is true only when both components are true. Treating A as incorrect contradicts the fundamental definition of conjunction.

Option C:
Option C is wrong because it adds D to the set of wrong statements, even though D accurately characterises “if and only if” as true when p and q share the same truth value. Including D among wrong statements undermines correct understanding of biconditional.

Option D:
Option D is also incorrect because by pairing B with C it misclassifies B, which correctly explains that inclusive “or” is false exactly when both disjuncts are false. This combination therefore rejects a correct connective rule.