UGC NET Questions (Paper – 1)

Statements A, B and C correctly define converse, inverse and contrapositive for a conditional, and E is true because an implication is logically equivalent to its contrapositive. D is false, as a conditional is not in general equivalent to its converse. Thus the complete set of correct statements about these relationships is A, B, C and E.

Option A:
Option A is incomplete because it omits E, failing to note the important fact that a conditional and its contrapositive are equivalent. Without E, the description of logical relations is not full. Therefore A, B and C only cannot be the correct answer.

Option B:
Option B is correct since it gathers the three accurate definitions and the key equivalence between the original implication and its contrapositive, while excluding D which overstates the relation to the converse. This matches standard treatments of conditionals used in UGC NET.

Option C:
Option C is incorrect because it includes D, which is false (a conditional is not always equivalent to its converse), and it also omits E, which is true. So it mixes a false statement with missing a true one.

Option D:
Option D is incorrect because it omits A, leaving out the explicit definition of the converse, and thus does not list all correct statements. Therefore B, C and E only is not acceptable.

Statement A correctly specifies that the contrapositive of “if p then q” is “if not q then not p”. Statement C is true because a statement and its contrapositive always have the same truth table and are logically equivalent. Statement D is also correct, as the inverse of “if p then q” is “if not p then not q”. Statement B is false because it actually describes the inverse, not the converse; the converse should be “if q then p”. Therefore, the correct set of statements is A, C and D only.

Option A:
Option A is incomplete since it omits D and therefore fails to state the form of the inverse, even though A and C are true. Without D, the picture of how all four related forms are constructed remains partial. This makes the option unsuitable as the correct answer.

Option B:
Option B is incorrect because it excludes C and includes D alone, leaving out the explicit mention of logical equivalence between contrapositives. It does not gather all the correct statements and so cannot represent the full answer.

Option C:
Option C is wrong as it puts together C and D but omits A, so it never explicitly defines the contrapositive itself, while still not distinguishing it from other forms. The missing definition makes this combination insufficient.

Option D:
Option D is correct because it lists the definition of contrapositive, the equivalence of contrapositives and the definition of inverse, while excluding the incorrect wording in B. It therefore gives a coherent and accurate summary of conditional variants.

Statement A pairs a conditional with its contrapositive, so they are logically equivalent. D is correct because logical equivalence by definition means matching truth values across all valuations. E is also true since a conditional and its contrapositive have identical truth conditions, so if the contrapositive is false, the original conditional must be false. B is wrong because its converse is not always true (an even number need not be divisible by 4), and C is wrong because a conditional is not generally equivalent to its converse. Thus A, D and E only form the correct combination.

Option A:
Option A is correct as it lists precisely the statements that capture equivalence with the contrapositive and the notion of equal truth values, while excluding B and C, which overstate the reliability of converses.

Option B:
Option B is incorrect because it adds B, which asserts that the converse of the divisibility statement is always true, even though simple counterexamples like 6 show this is false.

Option C:
Option C is wrong since it brings in C, which claims conditional and converse are always equivalent, contradicting standard logic, so the combination cannot be correct.

Option D:
Option D is incorrect as it omits A and includes B, thereby dropping a correct contrapositive-equivalence example and admitting a false statement about divisibility.

Statements A, B and C give the standard definitions of converse, contrapositive and inverse. Statement D is also correct because in classical logic a conditional and its contrapositive share the same truth table. Statement E is false; the converse need not be logically equivalent to the original conditional, as many counterexamples show. Hence the full and only correct collection is A, B, C and D, which appears in option B.

Option A:
Option A is incomplete because it omits D and thus fails to mention that a conditional and its contrapositive are equivalent in truth value. While A, B and C are true, they do not exhaust the set of correct statements.

Option B:
Option B is correct because it includes A, B, C and D, which are all true, and it excludes E, which is false because converse is not always equivalent to the original conditional.

Option C:
Option C is wrong because it includes E, which claims that the converse is always equivalent to the original statement. Since converse can change truth conditions, including E makes this combination incorrect.

Option D:
Option D is incorrect as it leaves out A. Although B, C and D are true, omitting A loses the correct description of converse, so this option does not list all correct statements.

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.

Statements A and C are correct because the contrapositive “If not q then not p” is logically equivalent to “If p then q”, and the inverse is indeed “If not p then not q”. Statement D is also true as many reasoning errors arise from confusing the converse “If q then p” with the contrapositive. Statement B is false because it mislabels the converse, and E is false because the contrapositive of a true implication is also true, not always false. Therefore, the combination A, C and D only is correct.

Option A:
Option A is correct since it gathers exactly the true statements about how converse, inverse and contrapositive are defined and how confusion among them can cause mistakes, while rejecting B and E, which misdescribe these relationships.

Option B:
Option B is incorrect as it includes B, which wrongly defines the converse, and thereby endorses a mislabelling of basic logical forms. Even though A and C are true, the presence of B ruins the option.

Option C:
Option C is wrong because it treats B, C and D as correct together, despite B being false. It also omits A, which explains the logical equivalence between an implication and its contrapositive, a central concept in NET-level logic.

Option D:
Option D is also incorrect because it includes E, which mistakenly claims that the contrapositive of a true implication is always false, and omits C, leaving out the correct statement of the inverse. This mixture makes the option unsound.

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.