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.

Statements A, B and C correctly define converse, inverse and contrapositive, while E and F state correct logical and exam-related facts, and D is false. A conditional is not equivalent to its converse, but it is equivalent to its contrapositive. When test-takers mistake a conditional for its converse, they often commit the fallacy of affirming the consequent. Therefore the set of correct statements is A, B, C, E and F only.

Option A:
Option A is incomplete because it omits F, leaving out the important note that this confusion gives rise to a specific fallacy tested in exams. While A, B, C and E are true, they do not mention the reasoning error that is pedagogically central. Hence this combination is not fully adequate.

Option B:
Option B is correct since it collects all the true statements about transformations of conditionals and their logical relations. It keeps the equivalence with the contrapositive and highlights the risk of misreading as a converse. By excluding D, which overstates equivalence, it stays faithful to standard logical theory.

Option C:
Option C is incorrect because it accepts D, wrongly claiming that a conditional is always equivalent to its converse. This would treat “If it is a square then it is a rectangle” as equivalent to “If it is a rectangle then it is a square”, which is not correct. Including D therefore makes the option unsound.

Option D:
Option D is wrong because it leaves out A and includes F but also omits one of the key definitional statements. Without A, the notion of converse is not clearly present, and the option does not gather all true statements. Thus it cannot be chosen as correct.

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 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.