UGC NET Questions (Paper – 1)

Statements A and B correctly define tautology and contradiction, D states that truth tables are a systematic method to classify statements and E rightly explains that contingent statements are sometimes true and sometimes false. Statement C is false because it mistakenly assigns the property of tautology to contingent statements by saying they are true in all situations. Consequently, A, B, D and E together form the only correct combination.

Option A:
Option A is correct because it lists exactly the statements that match standard logical definitions and excludes C, which confuses contingency with tautology. It reflects the approach used in UGC NET when analysing compound statements.

Option B:
Option B is incomplete since it omits E and therefore does not describe how contingent statements behave across different truth assignments. Without E, the classification of logical status is less complete.

Option C:
Option C is wrong because it leaves out A and thereby fails to define tautology explicitly, while still not correcting the misstatement about contingency. Although some included statements are true, the set is not complete.

Option D:
Option D is incorrect because it includes C, the false description of contingent statements, and so mixes an error with otherwise true statements. That mixture makes the option logically inconsistent.

Statements A, B and C describe standard facts about implication. A gives the important equivalence p → q ≡ ¬p ∨ q. B correctly states that an implication is false only when the antecedent is true and the consequent false. C correctly identifies the contrapositive as ¬q → ¬p. D is false because ¬p → ¬q is the inverse, not the converse, and E is false since p → q is generally not equivalent to q → p. Therefore A, B and C only are correct.

Option A:
Option A is incomplete because it omits C and thus fails to mention the contrapositive, which is central to reasoning with implications in many NET questions.

Option B:
Option B is incorrect as it includes D, which mislabels the inverse as the converse and therefore misuses terminology in logic.

Option C:
Option C is wrong because it omits A and therefore drops a key equivalence used to simplify implications.

Option D:
Option D is correct since it combines the truth-table characterisation of implication, the disjunctive form and the contrapositive, while excluding D and E, which contain conceptual errors about converse and equivalence.

Statements A, B, C and D give standard first-order logical translations of everyday sentences. A correctly uses a universal conditional for “all teachers are researchers”. B uses an existential statement with a conjunction for “some students are hardworking”. C appropriately translates “no books are boring” as a universal statement with a negated predicate. D is correct for “some teachers are not researchers” using an existential with a conjunction of teacher and not researcher. E is false because a universal statement does not, by itself, guarantee existence in formal logic, so A, B, C and D only are correct.

Option A:
Option A is incomplete since it omits D and therefore fails to include the important pattern for expressing “some S are not P” in quantifier form. Without D, the range of translation patterns is narrower than NET questions usually expect.

Option B:
Option B is correct because it gathers all four accurate translations and excludes E, which misinterprets what can be inferred from a universal statement alone. It reflects the standard mapping from natural language to quantified logic.

Option C:
Option C is wrong because it leaves out B, ignoring the existential construction for “some students are hardworking”, and still does not address E’s incorrect existential inference. As a result, it is not fully correct.

Option D:
Option D is incorrect since it includes E, which claims existence from a universal statement, an inference that is not valid in general first-order semantics, and also omits A, missing the core universal conditional pattern.

Statements A and C are correct because the contrapositive “If not q then not p” is logically equivalent to “If p then q”, and the inverse is indeed “If not p then not q”. Statement D is also true as many reasoning errors arise from confusing the converse “If q then p” with the contrapositive. Statement B is false because it mislabels the converse, and E is false because the contrapositive of a true implication is also true, not always false. Therefore, the combination A, C and D only is correct.

Option A:
Option A is correct since it gathers exactly the true statements about how converse, inverse and contrapositive are defined and how confusion among them can cause mistakes, while rejecting B and E, which misdescribe these relationships.

Option B:
Option B is incorrect as it includes B, which wrongly defines the converse, and thereby endorses a mislabelling of basic logical forms. Even though A and C are true, the presence of B ruins the option.

Option C:
Option C is wrong because it treats B, C and D as correct together, despite B being false. It also omits A, which explains the logical equivalence between an implication and its contrapositive, a central concept in NET-level logic.

Option D:
Option D is also incorrect because it includes E, which mistakenly claims that the contrapositive of a true implication is always false, and omits C, leaving out the correct statement of the inverse. This mixture makes the option unsound.

Statements A and B correctly describe the standard structure: two premises leading to a conclusion, each with subject and predicate terms. D is also correct because syllogistic validity concerns whether the conclusion follows logically from the premises, regardless of whether those premises are actually true. C is false since the middle term appears in the premises, not the conclusion, and E is false because a valid argument can have a true conclusion even when its premises are false. Therefore A, B and D only are correct.

Option A:
Option A is correct since it includes exactly the structural and logical-form facts without importing the false claims about the middle term and truth of premises forcing truth of conclusion.

Option B:
Option B is incorrect because it includes C, which mislocates the middle term in the conclusion instead of in the premises, so it puts a wrong statement into the combination.

Option C:
Option C is wrong as it adds E, which wrongly insists that false premises force a false conclusion, and it also fails to include B, so it contains errors/omissions.

Option D:
Option D is incorrect because although B and D are true, E is false, and dropping A loses the accurate description that a categorical syllogism has two premises and one conclusion.

Statements A, B, C and D correctly describe the relations of contrariety and subcontrariety in the traditional square, and F is true about exam usage. E is false because modern logic’s treatment of universal propositions without assumed existential import undermines some of the classical relationships. Thus the correct set of true statements is A, B, C, D and F only.

Option A:
Option A is correct since it includes all the accurate relational claims plus the observation that UGC NET may still use the traditional framework. It excludes E, which overstates the continuity between traditional and modern logic. This makes the option consistent with both history and syllabus.

Option B:
Option B is incomplete, as it omits F and therefore does not mention the exam context. While A, B, C and D are true, the option fails to cover all the correct statements listed.

Option C:
Option C is wrong because it includes E, which incorrectly claims that all traditional relations survive in modern treatment unchanged. This conflicts with standard modern logic texts, so the combination cannot be accepted.

Option D:
Option D is incorrect since it leaves out B, omitting the key general statement about contraries, and thus does not contain all true statements. Consequently, it does not represent the full correct set.

Statements A, B, C, E and F correctly distinguish tautologies, contradictions and contingencies and relate them to argument validity, while D is false. A tautological conclusion is always true, so any argument with such a conclusion is at least logically valid, though possibly uninformative. Contradictory premises render an argument vacuously valid because there is no case where all premises are true, and recognising logical status helps in judging equivalence and validity in exams. D is wrong because it asserts the opposite about tautological conclusions. Therefore A, B, C, E and F only is the correct combination.

Option A:
Option A is incomplete because it omits E and F, leaving out the role of contradictory premises and the exam-related significance of these distinctions. Although A, B and C are true definitions, they do not connect to argument validity. Thus this option is not complete.

Option B:
Option B is also incomplete, adding E but still omitting F, which summarises the practical usefulness of these categories in UGC NET. Without F, the option lacks an explicit link to reasoning tasks. Hence it cannot be the best answer.

Option C:
Option C is correct since it combines the basic definitions with a key fact about arguments from contradictions and the exam relevance of recognising logical status. It excludes D, which mischaracterises arguments with tautological conclusions. This makes the option logically consistent.

Option D:
Option D is incorrect because it includes D, thereby accepting the false view that tautological conclusions always make arguments invalid, and it omits A, the central definition of tautology. This combination cannot be taken as correct.

All five statements A through E are correct descriptions of standard logical classifications and their exam use. Tautologies are true under all assignments, contradictions are always false, and contingencies vary with the assignment. A statement and its negation cannot both be tautologies because their truth-values must differ somewhere. Recognising tautological patterns is useful in UGC NET for spotting valid argument forms.

Option A:
Option A is incomplete because it omits E, missing the applied exam-use point.

Option B:
Option B is correct since it includes every true statement (A–E).

Option C:
Option C is wrong because it omits C (definition of contingency).

Option D:
Option D is incorrect because it omits A (definition of tautology).

Statements A and B correctly define sufficient and necessary conditions by linking the holding of one property to the presence of another, and C is true because some conditions are both necessary and sufficient, forming a biconditional. Statement E is also true as many reasoning errors arise from confusing what is merely necessary with what is sufficient. Statement D is false because from “p is sufficient for q” it does not follow that q is sufficient for p; the implication generally does not reverse. Therefore, the correct combination is the one that collects A, B, C and E and excludes D.

Option A:
Option A is incomplete because it omits E and therefore does not acknowledge the common reasoning mistake of confusing necessary and sufficient conditions in practical thinking. While A, B and C are true, the set does not cover the full conceptual picture.

Option B:
Option B is also incomplete since it leaves out B, so it does not explicitly state how a necessary condition restricts the possibility of Q without P. Although A, C and E are true, missing B means the definition of necessity is not fully represented.

Option C:
Option C is correct because it gathers all true statements, including the definitional ones and the observation about everyday confusion, and it rightly rejects D, which incorrectly reverses the implication between sufficient conditions. This option best reflects the logic of conditionals.

Option D:
Option D is wrong because it includes D, which describes an invalid inference pattern, and it omits A, thereby failing to give the correct account of sufficiency. Mixing one false statement with an incomplete set of true ones makes this option unacceptable.

A correctly describes contradiction: assume the negation of what you want to prove and reach a contradiction. B is correct: proving the contrapositive is equivalent to proving the original conditional. D is correct: both are valid classical methods. C is false because contradiction proves the conclusion true (not both premises and conclusion false). E is false because contradiction proofs can be valid even when non-constructive. Therefore A, B and D only are correct.

Option A:
Option A is incomplete because it omits D, the statement confirming both methods are valid.

Option B:
Option B is incorrect because it includes C, which misstates the outcome of a contradiction proof.

Option C:
Option C is wrong because it omits A, leaving out the defining idea of contradiction.

Option D:
Option D is correct because it includes exactly the true statements and excludes C and E, which are false.

Statements A, B and C provide the standard classification of formulas into tautology, contradiction and contingency. Statement E is also true because truth tables are a systematic way to test which of these categories a formula falls into. Statement D is false because the existence of contingencies means there is indeed a third kind of formula. Therefore, A, B, C and E only make up the correct set.

Option A:
Option A is incomplete as it omits E and thus does not mention the main procedural tool, the truth table, which is central to exam questions on this topic.

Option B:
Option B is wrong since it includes D, which denies the existence of contingencies, contradicting statement C.

Option C:
Option C is correct because it captures all true statements and excludes D, which misclassifies propositional forms.

Option D:
Option D is incorrect as it retains D and omits A, losing the definition of tautology while including a false generalisation about all formulas.

Statements A, D and E correctly describe the nature of statement–argument questions and strong arguments. Statement B is wrong because emotional appeal alone does not make an argument strong if it lacks relevance or logic. Statement C is also wrong since candidates are expected to interpret and infer implied strengths or weaknesses, not just copy text. Therefore, the wrong statements are exactly B and C, which makes their combination the correct answer for this “select the wrong” question.

Option A:
Option A is incorrect because it isolates B as the only wrong statement and ignores C, even though C clearly misrepresents the need for interpretation and inference in these questions.

Option B:
Option B is also wrong because it singles out only C and overlooks B, which wrongly prioritises emotional appeal over logical relevance.

Option C:
Option C is incorrect because it wrongly treats D and E as wrong alongside B, even though D and E accurately characterise what counts as strong and how both supporting and opposing arguments are evaluated in NET exams.

Option D:
Option D is correct since it identifies B and C together as the problematic statements, while leaving A, D and E recognised as accurate descriptions of how statement–argument items work.

A is correct because logical equivalence is defined via matching truth values in all cases. B is true as p → q is truth-functionally the same as ¬p ∨ q. D is correct since a conditional and its contrapositive always share the same truth table. C is wrong because p → q and q → p are converses and need not share truth values, and E is wrong since equivalence is about truth conditions, not syntactic identity. Therefore, C and E only are the wrong statements.

Option A:
Option A is correct because it identifies exactly C and E as the problematic statements, leaving intact the proper definitions and equivalences in A, B and D. It aligns with standard logical theory taught for NET.

Option B:
Option B considers only C as wrong and mistakenly treats E as acceptable, despite E conflating syntactic form with semantic equivalence. It therefore misses one incorrect statement.

Option C:
Option C treats only E as wrong and ignores the clear counterexamples to C where p → q and q → p differ, so it does not cover all wrong statements.

Option D:
Option D includes D among wrong statements, even though D is correct about contrapositive equivalence, and so misclassifies a true principle along with the false ones.

A and B are correct definitions. C is false because valid arguments can have false premises. D is false because a true conclusion can come from invalid reasoning. E is false because a sound argument’s conclusion must be true. Thus only A and B are correct.

Option A:
Option A is incomplete because it omits B (soundness definition).

Option B:
Option B is correct because it includes exactly the two true statements.

Option C:
Option C is incorrect because it includes C (false).

Option D:
Option D is incorrect because it includes C and D (both false) and omits A.

Statement A is correct because “p sufficient for q” means p guarantees q, i.e., p → q. Statement B is correct because “p necessary for q” means q cannot hold without p, i.e., q → p. Statement C is true because mixing these up is a common reasoning error. Statement D is false (they are different), and E is false (contrapositive of p → q is ¬q → ¬p). Hence A, B and C only are correct.

Option A:
Option A is incomplete because it omits C (common error point).

Option B:
Option B is incomplete because it omits A (sufficiency mapping).

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

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