UGC NET Questions (Paper – 1)

Statements A, B and C correctly define simple, compound and categorical statements, and E is true about their relevance in symbolising arguments. D is false because compound statements can involve more than two components, such as “p and q and r”. F is false since an atomic statement by definition has no smaller independent statement-parts with their own truth values. Therefore the correct collection of true statements is A, B, C and E only.

Option A:
Option A is incorrect because it includes D, which wrongly restricts compound statements to exactly two components. That restriction does not hold in propositional logic where longer conjunctions and disjunctions are allowed. Hence this option mixes true and false statements.

Option B:
Option B is correct as it gathers all the accurate characterisations and the exam-related remark about symbolisation. It excludes D and F, both of which misrepresent the structure of simple and compound statements. This makes it the only fully consistent combination.

Option C:
Option C is wrong since it omits A, dropping the basic definition of a simple statement, and includes F, which falsely suggests divisibility of atomic sentences. As a result, the option does not contain all true statements and contains at least one false one.

Option D:
Option D is also incorrect because it includes D, preserving the mistaken limit on compound statements, and omits B, losing an essential part of the definition. This prevents the option from being correct.

A compound statement is formed when simpler statements are joined using logical connectives such as conjunction, disjunction or conditional. Its overall truth value depends on the truth values of the component statements and the nature of the connective. Propositional logic studies how these complex statements behave. Hence the kind of statement described in the stem is correctly called a compound statement.

Option A:
Option A, atomic statement, denotes a simple statement that is not built up from other statements and contains no logical connectives. It is the basic building block from which compound statements are constructed. Therefore it does not fit the description of being made from two or more simpler statements.

Option B:
Option B is correct because compound statements result from combining atomic propositions with connectives like “and” or “if...then”. Their complexity and truth conditions arise precisely from this combination, which is what the question highlights.

Option C:
Option C, predicate, is a term from predicate logic that refers to a property or relation that can be affirmed of objects. It is not itself the name for a whole statement constructed from simpler statements.

Option D:
Option D, categorical proposition, belongs to traditional logic and has the form “All S are P” or similar; although it can be complex, it is not defined simply by the presence of truth-functional connectives joining multiple simpler statements.

Conjunction is the compound statement formed by connecting two propositions with "and". According to its truth table, a conjunction is true only when each conjunct is true. This aligns with our intuitive understanding that both conditions must be met. Therefore the connective described in the question is correctly termed conjunction.

Option A:
Option A is correct because conjunction specifically denotes the logical operator that joins statements with "and" and demands the truth of all of them. It is one of the fundamental truth-functional connectives in propositional logic. The stem’s description matches this behaviour exactly.

Option B:
Option B, disjunction, connects statements with "or" and is usually interpreted in logic as true if at least one of the disjuncts is true. It does not require both components to be true, so it does not fit the question.

Option C:
Option C, implication, represents a conditional statement of the form "if p, then q". Its truth conditions differ significantly from those of conjunction and do not match the requirement that both parts be true.

Option D:
Option D, negation, operates on a single proposition by reversing its truth value. It does not combine two statements at all and thus cannot be the connective described.

A biconditional statement links two propositions in such a way that each implies the other. The form "p if and only if q" means that p is true exactly when q is true and false exactly when q is false. This captures a strong equivalence relation between the two. Therefore the compound statement described in the stem is called a biconditional.

Option A:
Option A, disjunctive, refers to a statement formed with "or", which is true when at least one of its disjuncts is true. It does not require mutual implication or matching truth values in the way a biconditional does. Hence disjunctive is not the correct answer.

Option B:
Option B, conjunctive, denotes a statement formed with "and" where both components must be true, but it does not capture the idea that each condition guarantees the other’s truth. Conjunction lacks the mutual equivalence of "if and only if".

Option C:
Option C, conditional, refers to one-way implication of the form "if p, then q". While a biconditional includes two such conditionals, the term conditional alone does not express the bi-directional nature specified in the question.

Option D:
Option D is correct because biconditional precisely names the connective that asserts "p if and only if q". Its truth table reflects equality of truth values between the component propositions and embodies logical equivalence.

Disjunction is the logical operation that forms a compound statement using "or". In its inclusive sense used in standard logic, a disjunction is true when at least one of the disjuncts is true and false only when both are false. This behaviour corresponds exactly to the description in the stem. Hence the connective is called disjunction.

Option A:
Option A, conjunction, links statements with "and" and is true only when both conjuncts are true. Its falsity conditions are therefore quite different and do not match the pattern described. Thus conjunction is not the correct answer.

Option B:
Option B is correct because disjunction accurately characterises the truth conditions stated: it fails only when neither component is true. This makes disjunction the appropriate technical term for the "or" connective in propositional logic.

Option C:
Option C, biconditional, expresses "p if and only if q" and is true when both components share the same truth value. This is more restrictive than the simple "or" relation and does not correspond to the stem.

Option D:
Option D, negation, alters the truth value of a single statement and does not combine two statements with "or". Consequently negation cannot be the intended connective.