UGC NET Questions (Paper – 1)

In propositional logic, the statement “if p, then q” is called a conditional or implication. It asserts that whenever p is true, q must also be true. This relation captures a directed dependence between antecedent and consequent. Therefore the connective in the stem is known as implication.

Option A:
Option A, biconditional, has the form “p if and only if q” and expresses a two-way equivalence. It is stronger than a simple conditional. Thus biconditional does not match the one-way “if p, then q” structure described here.

Option B:
Option B, disjunction, uses “or” to connect two statements and has different truth conditions. It does not encode a directional dependency from p to q. Hence disjunction cannot be the correct answer.

Option C:
Option C properly names implication as the connective that forms a conditional statement from an antecedent and a consequent. Its symbolisation as p → q corresponds exactly to “if p, then q”. Therefore implication is the best choice.

Option D:
Option D, conjunction, joins statements with “and” and requires both to be true. It lacks the conditional structure of premise leading to consequent. So conjunction is not the connective the question refers to.

The contrapositive of a conditional "if p, then q" is formed by negating both the antecedent and the consequent and reversing their positions, giving "if not q, then not p". In classical logic, a conditional and its contrapositive are always logically equivalent. This means they share the same truth table and stand or fall together. Hence the statement described is called the contrapositive.

Option A:
Option A, converse, yields "if q, then p" by swapping the antecedent and consequent without negating them. The converse is not necessarily equivalent to the original and thus does not match the pattern in the question.

Option B:
Option B, inverse, gives "if not p, then not q" by negating both parts but keeping their positions. Like the converse, the inverse is not generally equivalent to the original conditional. Therefore inverse is not the correct answer.

Option C:
Option C, biconditional, expresses "p if and only if q" and asserts both directions of implication in one statement. It is a different connective altogether and not merely a transformation of a single conditional.

Option D:
Option D is correct because contrapositive is the recognised name for the transformed conditional that is always logically equivalent to the original. This equivalence underlies many proof techniques.

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.

The contrapositive of a conditional “if p, then q” is the statement “if not q, then not p”. In classical logic, a conditional and its contrapositive are always logically equivalent. This means they share the same truth table and stand or fall together. Therefore the transformed statement described in the stem is called the contrapositive.

Option A:
Option A correctly names contrapositive as the form obtained by negating and swapping antecedent and consequent. Because it preserves logical equivalence, it is widely used in proofs. Hence this option accurately answers the question.

Option B:
Option B, converse, is “if q, then p”, which only swaps the positions without negating them. The converse is not guaranteed to be equivalent to the original conditional. Thus converse is not the correct label here.

Option C:
Option C, inverse, is “if not p, then not q”, which negates both parts but does not interchange them. Like the converse, it is generally not equivalent to the original statement. Therefore inverse does not fit the description.

Option D:
Option D, biconditional, has the form “p if and only if q” and requires both directions of implication. It is a different connective, not just a transformation of a single conditional. Hence biconditional is not appropriate.

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.

For an implication "If P, then Q," the contrapositive is "If not Q, then not P." These two statements are logically equivalent, meaning they are either both true or both false in every situation. The contrapositive reverses the direction of the implication and negates both the hypothesis and the conclusion. Therefore, the given statement "If not Q, then not P" is the contrapositive of "If P, then Q."

Option A:
The converse of "If P, then Q" is "If Q, then P," which merely swaps the positions of P and Q without negating them. It is not logically equivalent to the original statement in general. Since the given statement includes negations, it is not the converse.

Option B:
The inverse of "If P, then Q" is "If not P, then not Q," which negates both parts but keeps the order the same. This is different from "If not Q, then not P," which also reverses the roles of P and Q. Thus, the inverse is not the statement described in the question.

Option C:
The contrapositive is correct because it both negates and reverses the components of the original implication, matching the structure "If not Q, then not P." In logical reasoning, proving the contrapositive is a common technique for establishing the truth of an implication. Recognising this form is important for analysing arguments and proofs.

Option D:
A biconditional statement is of the form "P if and only if Q," signifying that P implies Q and Q implies P simultaneously. It does not involve the pattern "If not Q, then not P" as a standalone statement. Therefore, biconditional is not the correct term here.

In a conditional of the form “if p, then q”, the part that follows “if” is called the antecedent. It represents the condition under which the consequent is asserted to hold. Understanding which part is the antecedent is crucial for analysing implication, contrapositive and related logical forms. Thus the component p in the stem is correctly termed the antecedent.

Option A:
Option A is correct because antecedent literally means “that which goes before” and in conditional statements it precedes the “then” clause. It is the assumed or hypothetical part whose truth is taken as the basis for asserting the consequent.

Option B:
Option B, consequent, is the part that follows “then” and expresses what is said to follow from the antecedent. It corresponds to q, not to p, so it cannot be the answer here.

Option C:
Option C, premise, is a general term for any statement offered as a reason in an argument, and both antecedent and consequent can appear as premises in broader reasoning. However, premise does not specifically identify the first part of a conditional.

Option D:
Option D, conclusion, is the statement that the argument as a whole is trying to establish. A single conditional may express a premise or a conclusion, but p itself is not called the conclusion by definition.

This option is correct because the symbol '→' represents the logical conditional and is read as "implies." The statement "P → Q" is pronounced "P implies Q." It conveys that whenever P is true, Q must also be true. Therefore, the correct connective word is "implies."

Option A:
The phrase "P causes Q" suggests a causal relationship rather than a logical one. Logical implication does not necessarily assert any physical cause-and-effect link. Thus, "causes" is not the standard reading of the connective.

Option B:
In "P implies Q," "implies" is the accepted wording for the conditional statement. It indicates that truth of P guarantees truth of Q under the logical system. This matches the conventional reading of the symbol '→', so this option is correct.

Option C:
The phrase "P equals Q" refers to equality, which is represented by a different symbol, usually '='. It does not describe a conditional relation where one statement leads to another. Hence, this option is not appropriate.

Option D:
"P contradicts Q" would mean that P and Q cannot both be true, relating to negation rather than implication. That idea is closer to exclusive or or inconsistency, not the ordinary conditional statement. Therefore, this option is incorrect.

Statement A is correct because “p sufficient for q” means p guarantees q, i.e., p → q. Statement B is correct because “p necessary for q” means q cannot hold without p, i.e., q → p. Statement C is true because mixing these up is a common reasoning error. Statement D is false (they are different), and E is false (contrapositive of p → q is ¬q → ¬p). Hence A, B and C only are correct.

Option A:
Option A is incomplete because it omits C (common error point).

Option B:
Option B is incomplete because it omits A (sufficiency mapping).

Option C:
Option C is correct since it includes all true statements and excludes D and E.

Option D:
Option D is incorrect because it includes D (false) and omits B (true).