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.

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.

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.

Statements D and E are wrong, while A, B, C and F are correct. A and B correctly describe the truth conditions for conjunction and inclusive disjunction, and C accurately symbolises the exclusive “either–or”. F is true because truth tables are standard tools for checking validity. D mistakenly describes a tautology instead of a contradiction, and E wrongly describes the condition for a contingent statement rather than a tautology, so these two are the wrong statements.

Option A:
Option A is incorrect because it singles out only D as wrong and ignores E, which also misrepresents the definition of a tautology. Since both D and E give inverted definitions, treating only one of them as wrong undercounts the errors. Therefore this option does not match the full set of wrong statements.

Option B:
Option B is also incomplete, as it selects only E and ignores D. D is clearly false because a contradiction is never true in any assignment, not always true. By failing to include D, this option again fails to capture all wrong statements listed.

Option C:
Option C is correct because it groups exactly D and E, the two statements that invert the standard meanings of contradiction and tautology. It leaves A, B, C and F untouched, all of which correctly describe truth-functional connectives and the use of truth tables. This combination therefore matches the required set of wrong statements.

Option D:
Option D is wrong because it adds B, which is a correct description of inclusive disjunction, to the set of wrong statements. B rightly states that “p or q” is false only when both p and q are false. Including B beside the genuinely wrong D and E makes the option logically inconsistent.

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.

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.

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.

Statements A, B and C are all correct. A notes the common natural-language use of “either” as exclusive. B is true because the standard logical disjunction is inclusive and allows both A and B to be true. C correctly gives a formula for exclusive-or using OR, AND and NOT. D is false since exam questions may clarify whether the sense is inclusive or exclusive, and E is false because inclusive and exclusive or differ when both A and B are true. Hence, A, B and C only are correct.

Option A:
Option A is incomplete since it omits C, thereby failing to mention the formal definition of exclusive-or in terms of other connectives, which is important in logical reasoning.

Option B:
Option B is incorrect because it incorrectly includes D, which claims that exam usage is always exclusive, and so introduces a false constraint on interpretation.

Option C:
Option C is correct as it combines natural-language usage, the inclusive logical meaning and the formal construction of exclusive-or, while excluding D and E, which misstate exam conventions and truth-value patterns.

Option D:
Option D is wrong since it includes E, which wrongly claims that inclusive and exclusive or always agree, and it drops A, losing the important point about everyday interpretation.

B, C and E are correct; A and D are false. A simple proposition has no logical connective; compound propositions use connectives. “It is raining and it is cold” is compound; “It is raining” is simple. Recognising this helps symbolic translation in UGC NET.

Option A:
Option A is incorrect because it includes A, which wrongly says a simple proposition contains a connective.

Option B:
Option B is incomplete because it omits E (exam translation relevance), which is true.

Option C:
Option C is correct because it includes all true statements (B, C, E) and excludes A and D (false).

Option D:
Option D is incorrect because it includes A and D, which are false.

Negation is the unary operation that takes a proposition and forms a new proposition that is true exactly when the original is false and false when the original is true. In symbolic logic, it is often represented by a tilde or a bar. Negation allows us to express denial or refusal within formal systems. Therefore the operation described is correctly called negation.

Option A:
Option A, implication, relates two propositions in a conditional structure "if p, then q" and does not simply reverse a truth value. It is a binary connective rather than a single-place operation. Thus implication does not fit the stem.

Option B:
Option B, equivalence, concerns a relation between two propositions that have the same truth value. It is not an operation that individually flips a truth value. Consequently equivalence is not appropriate here.

Option C:
Option C is correct because negation captures precisely the idea of truth-value reversal expressed in the question. The operation is fundamental in constructing logical opposites and in formulating contradictions.

Option D:
Option D, disjunction, joins two propositions with "or" and has truth conditions based on at least one disjunct being true. It does not operate on just one statement, so it cannot be the operation sought in the stem.

Statement C is wrong because in standard truth-functional logic the conditional “if p then q” is false precisely when p is true and q is false, not when p is false and q is true. Statements A and B correctly describe the conditions for truth of conjunction and inclusive disjunction, while D accurately explains the biconditional and E states the essential idea that compound truth values depend on component truth values. Hence, C alone is the incorrect statement, so the option that lists only C is correct.

Option A:
Option A is correct since it identifies C as the sole misstatement and implicitly accepts A, B, D and E as standard truth-table definitions. It preserves the conventional semantics of implication while rejecting the inverted condition given in C.

Option B:
Option B is incorrect because it also labels A as wrong, even though A correctly states that “p and q” is true only when both components are true. Treating A as incorrect contradicts the fundamental definition of conjunction.

Option C:
Option C is wrong because it adds D to the set of wrong statements, even though D accurately characterises “if and only if” as true when p and q share the same truth value. Including D among wrong statements undermines correct understanding of biconditional.

Option D:
Option D is also incorrect because by pairing B with C it misclassifies B, which correctly explains that inclusive “or” is false exactly when both disjuncts are false. This combination therefore rejects a correct connective rule.

A statement that is always true under every possible assignment of truth values to its components is called a tautology. The disjunction “p or not p” covers all possibilities: if p is true, the first part is true; if p is false, not p is true. Thus, in all cases the compound statement evaluates to true. This makes “p or not p” a classic example of a tautology.

Option A:
Option A, “p and not p,” is instead a contradiction because it asserts that p is both true and false simultaneously. There is no assignment of truth values that can make both p and not p true together, so this statement is never true.

Option B:
Option B, “p or not p,” correctly spans all truth possibilities for p. Since one of p or not p must be true, their disjunction is always true, demonstrating tautological status.

Option C:
Option C, “p → not p,” is not always true. If p is true, the implication would require not p to be true as well, which is impossible, so the statement can be false.

Option D:
Option D, “not p → p,” also fails to be always true; there are assignments where it becomes false, so it is not a tautology.

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.

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.