UGC NET Questions (Paper – 1)

Statements A and B give the standard truth conditions for conjunction and inclusive disjunction. Statement D is correct because p → q is equivalent to ¬p ∨ q in classical logic. Statement E is also true since connectives allow us to build complex propositions from atomic ones. Statement C is false because ¬p is true when p is false, not when p is true. Thus A, B, D and E only form the correct set.

Option A:
Option A is incomplete as it omits E and therefore does not mention the important role of connectives in constructing compound statements, even though A, B and D are true.

Option B:
Option B is correct since it includes all true statements and excludes C, which reverses the meaning of negation. It matches the truth-table definitions that NET candidates must know.

Option C:
Option C is incorrect because it contains C, the wrong description of negation, despite including some true statements, so the overall set cannot be accepted.

Option D:
Option D is also wrong as it retains C and omits A, losing the clear definition of conjunction while endorsing an incorrect statement about negation.

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.

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.