UGC NET Questions (Paper – 1)

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.

A, B, C and E are correct. D is false because natural language uses of “if/only if” can be looser than strict logical operators. Therefore the correct combination is A, B, C and E only.

Option A:
Option A is incomplete because it omits E (exam translation importance).

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

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

Option D:
Option D is incorrect because it omits A, so it is incomplete.

Statements A, B, C and E correctly state the truth conditions and logical role of biconditionals, while D is false. “If and only if” requires that p and q share the same truth value, which can be expressed as two conditionals taken together. It is false exactly when one is true and the other false. Far from being only sufficient, p is both necessary and sufficient for q in a biconditional, so D misdescribes the relation. Recognising this helps with equivalence transformations in UGC NET questions.

Option A:
Option A is incomplete because it omits E, not mentioning how biconditionals feature in exam-style equivalence problems. A, B, C only therefore leaves out a key application of the concept.

Option B:
Option B is wrong since it drops A, thereby failing to state in general that biconditionals are true when p and q match in truth value. B, C, E only provides specific and exam-related facts but lacks the core truth-condition statement.

Option C:
Option C is correct as it gathers all the true statements and excludes D, which restricts the relation to sufficiency alone. This option aligns with standard propositional logic and how biconditionals are tested in symbolic reasoning questions.

Option D:
Option D is incorrect because it omits B, losing the important equivalence of a biconditional with two conditionals. A, C, E only is therefore not acceptable as the right answer.

A, B and E are correct; C and D are wrong. Denying the antecedent and affirming the consequent are invalid forms; only modus ponens and modus tollens are valid. UGC NET tests spotting these invalid patterns.

Option A:
Option A is incorrect because D is also wrong; selecting only C is incomplete.

Option B:
Option B is incorrect because C is also wrong; selecting only D is incomplete.

Option C:
Option C is incorrect because B is correct (modus tollens), so including B as wrong is incorrect.

Option D:
Option D is correct because it identifies both invalid patterns (C and D) as wrong.

Statements A, B, C and D correctly describe how “unless” is handled in logical translation, while E is false. “p unless q” can be read as “if not q then p”, and this in turn is equivalent to “p or q”, often represented with “or” and negation in symbols. Mishandling this connective, such as turning it into “if p then q”, leads to incorrect formalisation in exam problems. Therefore, the correct set includes A, B, C and D only.

Option A:
Option A is incomplete because it omits D, not acknowledging the exam-specific warning that mistranslating “unless” leads to errors. A, B, C only therefore does not fully address the question’s focus on UGC NET practice.

Option B:
Option B is wrong since it leaves out A, losing the general point that “unless” is captured using “or” and negation in symbolic notation. B, C, D only therefore presents only a partial description.

Option C:
Option C is correct as it includes the definitional, equivalence and exam-oriented statements while excluding E, which mistakenly equates “unless” with a one-way conditional. This combination matches standard treatments in logic textbooks.

Option D:
Option D is incorrect because it omits B and thus fails to mention the key equivalence “if not q then p”, central to understanding “unless”. A, C, D only therefore cannot be the right answer.

All five statements are correct: truth tables enumerate combinations, test validity via true-premise/false-conclusion rows, identify tautologies by all-true columns, require 2³ = 8 rows for three variables, and underpin many exam solutions even when not drawn.

Option A:
Option A is incomplete because it omits E (implicit exam use).

Option B:
Option B is incomplete because it omits D (8-row fact for three variables).

Option C:
Option C is correct because it includes all true statements (A–E).

Option D:
Option D is incorrect because it omits A (the basic definition of what truth tables do).

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.

Statements A, B, C and E are correct, while D is false. The law of excluded middle asserts that for any proposition p, either p or ¬p holds in classical two-valued logic, with no third option. Some non-classical systems, such as intuitionistic logic, restrict or reject this law in certain contexts, which supports C. In classical logic, “p ∨ ¬p” is a tautology, not a contradiction, so D mislabels it. UGC NET logic questions frequently refer to excluded middle and non-contradiction, as E indicates. Therefore A, B, C, E only is the correct set.

Option A:
Option A is incomplete since it omits E, not mentioning the exam’s interest in these fundamental laws. A, B, C only therefore does not fully satisfy the stem.

Option B:
Option B is wrong because it leaves out C, failing to acknowledge that some non-classical logics challenge the universal scope of excluded middle. A, B, E only thus presents too narrow a view.

Option C:
Option C is incorrect as it omits A and thereby fails to state the law itself, giving only its context and exam relevance. B, C, E only therefore does not directly identify excluded middle.

Option D:
Option D is correct because it collects the accurate statements about the law, its classical role, its non-classical challenges and its exam importance while excluding D, which wrongly calls “p ∨ ¬p” a contradiction. This selection matches standard introductions to logic and UGC NET-level treatments.

Statements A, B, D and E are correct, while C is false. A tautology is true under every valuation and a contradiction is false under every valuation. A contingent statement is true in some valuations and false in others, so C is incorrect. If a conclusion is a tautology, there is no possible case where premises are true and the conclusion is false, so the argument is valid regardless of premises (though it may be uninformative). Distinguishing these notions helps in validity checking in UGC NET, so E is also correct.

Option A:
Option A is incorrect because it omits D. Since D is true in classical logic, A, B, E only is incomplete.

Option B:
Option B is correct because it includes exactly the true statements A, B, D and E and excludes C, which misdefines contingency.

Option C:
Option C is wrong because it includes C, the false claim that a contingent statement is true in all valuations.

Option D:
Option D is wrong because it includes C (false) and omits B (true), so A, C, D, E only cannot be correct.

A, B, C and E are correct; D is false. “p ∧ (q ∨ r)” distributes to “(p ∧ q) ∨ (p ∧ r)”, not just “(p ∧ q)”. Standard equivalences (A–C) and their use (E) are correct.

Option A:
Option A is incorrect because A is correct; grouping it with D as wrong is incorrect.

Option B:
Option B is correct because D is the only wrong statement.

Option C:
Option C is incorrect because C is correct; adding it to the wrong set is incorrect.

Option D:
Option D is incorrect because B and E are correct; treating them as wrong is incorrect.

Statements A, B, C and E correctly describe the truth-table method for testing validity, while D is false. Validity depends on what happens in all rows where premises are true: if the conclusion is always true in those rows, the argument form is valid; if there is even one row with true premises and a false conclusion, the form is invalid. We therefore must systematically inspect all such rows, not just one arbitrarily chosen row. In UGC NET, many candidates reason through small tables mentally, illustrating E.

Option A:
Option A is incomplete as it omits E, not acknowledging that mental truth-table reasoning is often used in the exam. A, B, C only therefore does not fully incorporate the exam-oriented aspect of the question.

Option B:
Option B is wrong because it leaves out C, neglecting the explicit description of the counterexample row that makes a form invalid. A, B, E only thus fails to give the full condition for invalidity.

Option C:
Option C is correct since it combines the method for finding rows with true premises, the criteria for validity and invalidity, and the exam practice of mental truth tables while excluding D. It reflects standard teaching and UGC NET expectations.

Option D:
Option D is incorrect because it omits A and claims that inspecting only one arbitrary row is sufficient, which contradicts the requirement to check all rows where premises are true. B, C, E only therefore cannot be correct.