UGC NET Questions (Paper – 1)

Statements A, B, D and E are correct, whereas C and F are false. Simple statements have no smaller statement parts, and compound statements are built from them with connectives. Negation does flip truth values in classical logic, and each atomic statement gets its own column in a truth table. C is wrong because connectives also determine how component truth values combine, and F is wrong because UGC NET questions frequently use compound statements.

Option A:
Option A is incorrect because it leaves out statement E, which accurately describes how truth tables are constructed. While A, B and D are true, omitting E means the answer does not include all correct statements. The description of truth-table practice is therefore incomplete in this option.

Option B:
Option B is correct since it brings together A, B, D and E, the four statements that match standard propositional logic. It excludes C, which ignores the role of connectives, and F, which falsely denies the presence of compound statements in exam questions. This combination therefore reflects both theory and examination practice.

Option C:
Option C is wrong because it includes C along with otherwise correct statements. C claims that connectives do not matter for truth values, which contradicts the whole idea of truth-functional operators. Adding a false statement makes the entire combination unacceptable.

Option D:
Option D is incorrect because it omits A, the basic definition of a simple statement, and it starts from B. Although B, D and E are true, without A the picture of the distinction between simple and compound statements is incomplete. Thus this option fails to represent the full set of correct statements.

Conjunction is the compound statement formed by joining two propositions with “and”. It is defined to be true only when each of its component propositions is true. This truth-functional behaviour is central to classical propositional logic. Therefore the connective described in the stem is correctly called conjunction.

Option A:
Option A, disjunction, is formed using “or” and is usually true when at least one of its components is true. It does not require both components to be true simultaneously. Hence disjunction does not match the condition specified in the question.

Option B:
Option B correctly identifies conjunction as the connective that yields truth only when both conjuncts are true. This exclusive requirement distinguishes it from other connectives. Thus conjunction is the most appropriate answer here.

Option C:
Option C, implication, represents a conditional of the form “if p, then q”. Its truth conditions do not restrict both parts to be true. Therefore implication is not the connective being described.

Option D:
Option D, negation, simply reverses the truth value of a single proposition. It does not join two propositions and so fails to fit the description given in the stem.

A contradiction is a statement that is false under every possible assignment of truth values to its variables. The expression P ∧ ¬P asserts that P is both true and not true at the same time, which cannot occur. In any valuation, either P is true or P is false; in neither case can the conjunction of P and its negation be true. Hence this expression is always false and is a standard example of contradiction.

Option A:
Option A directly combines a proposition with its own negation using “and,” ensuring that no scenario makes the whole statement true.

Option B:
Option B, P ∨ ¬P, is actually a tautology, as it is always true regardless of P’s value.

Option C:
Option C can be true or false depending on the values of P and Q, so it is a contingency, not a permanent contradiction.

Option D:
Option D, P → Q, is also contingent; its truth depends on how P and Q are valued.

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.

In propositional logic, the connective “and” corresponds to conjunction. A conjunction p and q is true only when both component statements p and q are true simultaneously. Here p says the number is even and q says it is divisible by 3. Putting them together with “and” requires both properties to hold. Thus, the combined statement means that the number must be even and divisible by 3.

Option A:
Option A uses “or” instead of “and,” which corresponds to a different connective (disjunction). It allows numbers that are only even or only divisible by 3, and hence does not capture the meaning of “p and q.”

Option B:
Option B mixes “either” with a negation in a way that is not equivalent to the original conjunction. It introduces “not divisible by 3,” which is not part of q.

Option C:
Option C reflects the standard interpretation of a logical conjunction: both conditions must be simultaneously satisfied. It directly translates “p and q” into ordinary language as “even and divisible by 3.”

Option D:
Option D makes both properties false, which would correspond to the negation of p and q, not the conjunction of p and q.