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.

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.

Two propositions are logically equivalent when they share the same truth value in all possible circumstances. A joint truth table reveals this by showing matching columns for the two statements on every row. Logical equivalence means that each proposition implies the other, so they stand or fall together. Accordingly, the relationship described in the stem is that of logical equivalence.

Option A:
Option A is correct because logical equivalence formalises the idea of identical truth behaviour across all valuations. This relation can also be expressed using a biconditional, reflecting mutual implication. The truth-table condition in the question is the standard test for such equivalence.

Option B:
Option B, contradictory, would require that one proposition be true whenever the other is false and vice versa. This implies opposite truth values on every row, not identical ones. Therefore contradiction is not what the stem describes.

Option C:
Option C, inconsistent, typically refers to a set of propositions that cannot all be true together. It does not describe a relation between two single propositions having matching truth values under all conditions. Hence inconsistent is not appropriate here.

Option D:
Option D, independent, suggests that the truth of one proposition has no fixed effect on the truth of the other, so their truth values are not reliably correlated. This is the opposite situation to having identical truth values on every row.

Statements A, B, C and E correctly characterise truth-functional connectives and their exam role, while D is false. A connective like “and” or “or” yields compound truth values determined entirely by the truth of their components, and truth tables provide a systematic way to evaluate them. “Because” is generally not treated as a purely truth-functional connective at this level, as it carries causal or explanatory content. Thus A, B, C and E only gives the complete set of correct statements.

Option A:
Option A is incomplete because it drops E, failing to mention the practical utility of this knowledge in UGC NET truth-table questions. A, B, C only therefore does not fully reflect the exam-focused part of the stem.

Option B:
Option B is wrong since it omits A, the general definition of a truth-functional connective, leaving only specific examples and exam commentary. B, C, E only thus lacks the conceptual core that defines what these connectives are.

Option C:
Option C is incorrect because it includes A and C and E but leaves out B, so it does not explicitly state that “and”, “or” and “if…then” are the typical connectives used in UGC NET symbolic logic. A, C, E only is therefore incomplete.

Option D:
Option D is correct as it includes all the true statements and excludes D, which wrongly promotes “because” to the status of a standard truth-functional symbol. This combination matches textbook treatments and exam expectations.

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 tautology is a formula that evaluates to true on every row of its truth table, regardless of how its component propositions are valued. Its truth depends purely on its logical form, not on any contingent facts. Tautologies serve as logical truths that cannot be denied without inconsistency. Thus the compound statement described in the stem is a tautology.

Option A:
Option A, contradiction, is the opposite extreme: a statement that is false under every possible valuation. It cannot ever be true, which does not match the always-true condition in the question. Therefore contradiction is not correct.

Option B:
Option B, contingency, may be true under some valuations and false under others. Its truth is not fixed across all possibilities, so it fails to meet the "true under every" condition. Thus contingency is not appropriate here.

Option C:
Option C, paradox, is an informal term for statements that seem self-contradictory or counterintuitive but may contain a deeper truth. Paradoxes are not defined simply by their truth table behaviour. Consequently paradox does not answer the question.

Option D:
Option D is correct because tautology exactly captures the notion of a statement that cannot come out false on any truth-value assignment. Such statements are central to proofs and equivalence tests in logic.

Modus tollens is the valid rule that allows us to infer the negation of the antecedent from a conditional and the negation of its consequent. In symbolic form, from P → Q and ¬Q we conclude ¬P. This pattern preserves validity, because if P had been true, Q would have had to be true as well, so the falsity of Q forces the falsity of P.

Option A:
Option A is modus ponens, which affirms the antecedent to derive the consequent, a different valid pattern.

Option B:
Option B commits the fallacy of denying the antecedent, which is not generally valid.

Option C:
Option C correctly captures the modus tollens form, using the falsity of the consequent to infer the falsity of the antecedent.

Option D:
Option D is the fallacy of affirming the consequent, which is invalid in general.

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.

A tautology is a statement that is true under every assignment of truth values to its components. Its truth is guaranteed by its logical form alone. Such statements are logically necessary and cannot be false. Therefore the description in the stem matches the concept of a tautology.

Option A:
Option A, contradiction, is always false under every possible valuation. It represents the opposite logical extreme from a tautology. Hence contradiction does not fit the stem.

Option B:
Option B, contingency, is a statement that is true under some valuations and false under others. Its truth is not fixed across all possibilities. Therefore contingency is not the correct answer here.

Option C:
Option C correctly names tautology as the always true compound statement described. Tautologies play an important role in logical equivalence and proof. Thus tautology is the appropriate choice.

Option D:
Option D, paradox, refers informally to a statement that seems self-contradictory or absurd yet often reveals a truth. It is not defined as a statement true in all valuations. Consequently paradox is not suitable here.

A contradiction is a statement that cannot be true under any assignment of truth values to its components. Its logical form guarantees falsity in every possible case. Such statements are logically impossible and indicate inconsistency. Therefore the compound statement described in the stem is a contradiction.

Option A:
Option A, tautology, is always true and thus stands opposite to contradiction. It does not match the condition of being false in all valuations. Hence tautology is not the correct answer.

Option B:
Option B, contingency, can be true in some cases and false in others. It lacks the universal falsity required by the stem. Therefore contingency is not appropriate here.

Option C:
Option C, paradox, is an informal term for seemingly self-contradictory statements, but not every paradox is logically false under all valuations. The stem instead describes the technical notion of contradiction. Thus paradox is not the best label.

Option D:
Option D correctly names contradiction as the form that is false in every possible situation. Recognising contradictions is crucial for testing the consistency of logical systems. Hence contradiction is the correct choice.

A truth functional connective is defined by the way it systematically turns combinations of truth values of component statements into a truth value for the whole. For such connectives, once the truth values of the parts are known, the truth of the compound is completely determined. Examples include conjunction, disjunction, conditional and biconditional as studied in truth tables. Thus the connective described in the stem is properly called truth functional.

Option A:
Option A, intensional, usually refers to expressions whose meaning involves more than just extension or truth value, such as belief operators, and so is not restricted to connectives determined purely by truth values. Intensional contexts often break straightforward truth-functionality. Therefore intensional is not the correct label here.

Option B:
Option B is correct because truth functional connectives behave exactly as the stem describes: their semantic contribution can be fully represented in a truth table. This makes them central to classical propositional logic.

Option C:
Option C, non truth functional, would describe connectives or operators whose effect cannot be captured solely by reference to the truth values of component statements, which is the opposite of what the question states.

Option D:
Option D, analogical, has to do with reasoning by analogy between cases rather than with how connectives determine truth values. It is unrelated to the technical notion of truth-functionality.

De Morgan’s laws state that the negation of a disjunction is equivalent to the conjunction of the negations: Not (P or Q) is the same as (Not P) and (Not Q). Intuitively, saying “it is not the case that P or Q” means that neither P is true nor Q is true. The resulting statement is stronger than simply denying one of them; it requires both to be false. This equivalence holds for all combinations of truth values of P and Q.

Option A:
Option A correctly replaces the outer negated “or” with an “and” of the separate negations, in line with the formal statement of De Morgan’s law for disjunction.

Option B:
Option B would express the negation of a conjunction, Not (P and Q), rather than Not (P or Q), and is therefore the wrong transformation.

Option C:
Option C adds a biconditional between the negations, which is not equivalent to negating the disjunction.

Option D:
Option D introduces an implication relation between the negations, which again has a different truth table from the negation of P or Q.

The contrapositive of a conditional “If P then Q” is “If not Q then not P.” It is logically equivalent to the original statement. Here, P is “it is a bird” and Q is “it can fly.” Negating Q gives “it cannot fly,” and negating P gives “it is not a bird.” Therefore, the contrapositive is “If it cannot fly, then it is not a bird,” which preserves the truth conditions of the original conditional.

Option A:
Option A follows the correct procedure of reversing and negating both the antecedent and consequent. It captures the idea that anything that fails the flight condition cannot belong to the bird category under this rule.

Option B:
Option B is the converse, “If Q then P,” which is not guaranteed to be equivalent; many non birds can fly.

Option C:
Option C is the inverse, “If not P then not Q,” which is also not equivalent and can be false even if the original is true.

Option D:
Option D contradicts the original conditional by stating that non birds can fly as a rule, which is unrelated to the given statement.

A tautology is a compound proposition that evaluates to true under every possible assignment of truth values to its component propositions. It is logically true by virtue of its form rather than specific factual content. In a full truth table, the column for a tautology’s final result contains only Ts and no Fs. Because of this feature, tautologies play an important role in testing argument forms and deriving equivalences.

Option A:
Option A matches the formal definition of a tautology as a statement that never turns out false in any row of its truth table. It captures the idea of logical necessity independent of empirical facts.

Option B:
Option B describes a contradiction, which is always false and has only Fs in its truth table, the exact opposite of a tautology.

Option C:
Option C refers to a contingency, which is true on some valuations and false on others, so it is neither tautological nor contradictory.

Option D:
Option D suggests that the statement cannot be tested, which is incorrect because tautologies are routinely checked using truth tables and formal methods.

A contradiction is a statement that cannot be true in any possible situation because its form guarantees falsity on every line of its truth table. It is logically inconsistent and unsatisfiable, meaning no assignment of truth values makes it hold. Such statements often arise from combining a claim and its negation. Therefore the statement described in the stem is accurately called a contradiction.

Option A:
Option A is correct because contradictions exhibit the extreme case of logical falsity: they are false in all possible worlds or under all valuations. Recognising contradictions is important in proofs by contradiction and in detecting inconsistent sets of premises.

Option B:
Option B, tautology, is the exact opposite: a statement that is true under every possible assignment of truth values. While it also has a uniform truth-value pattern, that pattern is truth rather than falsehood.

Option C:
Option C, contingency, is true under some assignments and false under others, which is the normal status of most factual claims. The stem, however, speaks of a statement that is false in every possible case.

Option D:
Option D, hypothesis, refers to a provisional assumption or conjecture and does not specify a particular truth-table pattern. A hypothesis could be a tautology, contradiction or contingency depending on its logical form and content.