UGC NET Questions (Paper – 1)

Statements A, B, C and D correctly relate “if”, “only if” and necessary conditions to their symbolic forms, and F is also true, while E is false. The biconditional is true exactly when p and q share the same truth value, not when they differ. Treating “only if” carefully is crucial for distinguishing what is necessary from what is sufficient. Hence the correct set of statements is A, B, C, D and F only.

Option A:
Option A is incomplete because it omits D and F, leaving out both the explicit link to necessary conditions and the exam relevance of misreading “only if”. Although A, B, C and E mention some relationships, they include E, which wrongly states the truth pattern of the biconditional. This makes the option incorrect.

Option B:
Option B is wrong because it includes E, which claims that “p if and only if q” is true when p and q differ in truth value. That is the truth condition for exclusive disjunction, not for the biconditional. Including E makes the combination logically inconsistent.

Option C:
Option C is correct as it gathers A, B, C and D, which correctly express equivalences and necessary condition symbolism, and F, which notes the importance of reading these connectives properly in exams. It excludes E, avoiding the confusion between biconditional and exclusive or. This matches standard logical teaching.

Option D:
Option D is incorrect since it omits A and replaces it with B, C, D, E and F. Without A, the equivalence of “p only if q” with “If p then q” is not stated, and including E still misrepresents the truth conditions of the biconditional. Therefore it cannot be the right answer.

Statements A, B and C correctly define sufficient and necessary conditions and note that a condition can sometimes be both. E is also true because many exam questions exploit this confusion. D is false, since “only if” generally indicates a necessary condition, not a sufficient one. Therefore the correct set of true statements is A, B, C and E only.

Option A:
Option A is correct because it includes all the accurate definitional statements and the exam-focused remark, while excluding D which reverses the usual reading of “only if”. It captures both conceptual clarity and test relevance.

Option B:
Option B is incomplete as it leaves out C, ignoring cases where a condition is both necessary and sufficient, so it does not gather all correct statements.

Option C:
Option C omits A, failing to state what a sufficient condition does, and therefore cannot be fully correct even though it retains some true statements.

Option D:
Option D excludes B, losing the definition of a necessary condition, so A, C and E only does not contain all true statements.

A necessary condition must be present whenever the outcome occurs. If having a valid admit card is necessary for entry, then anyone who is inside the hall must have such a card. In conditional form this becomes “If a person enters the hall, then the person has a valid admit card.” The statement does not claim that possessing a card alone is enough for entry, only that entry cannot happen without it.

Option A:
Option A treats possessing the card as sufficient for entry, which goes beyond necessity and may ignore other requirements like identity proof.

Option B:
Option B captures the idea that entry implies the presence of the necessary condition, aligning with the logical form “Outcome → Condition.”

Option C:
Option C reverses the direction in a way that ties receiving the card to entering, which is not what the original statement asserts.

Option D:
Option D explicitly mislabels the condition as sufficient but not necessary, contradicting the claim that it is necessary.

Statements A, B, C and E correctly state how necessary and sufficient conditions function, while D is false. A necessary condition must be present for the effect, and a sufficient condition guarantees the effect when it occurs. In some cases, a condition can be both necessary and sufficient, as with logical equivalences. If X is genuinely necessary for Y, Y cannot occur without X, so D contradicts the definition. UGC NET cause–effect and assumption questions often hinge on these distinctions, validating E.

Option A:
Option A is incomplete because it leaves out C and E, omitting both the possibility of conditions being both ways and the explicit exam relevance. A, B only therefore does not provide the full information intended.

Option B:
Option B improves on A but still omits E, failing to note that these notions are directly examined in UGC NET reasoning. A, B, C only thus remains incomplete with respect to the stem.

Option C:
Option C is wrong as it drops A and incorrectly suggests that specifying B, C, E alone is enough while excluding the basic role of necessary conditions. B, C, E only gives an unbalanced picture of the concepts.

Option D:
Option D is correct since it includes all true statements and excludes D, which misdescribes the relation of necessity. This aligns with standard logic and analytical reasoning used in exam questions.

Saying that something is sufficient for an outcome means that whenever that condition holds, the outcome is guaranteed. If having a ticket is sufficient to enter, then anyone with a ticket qualifies for entry, even though there might be other ways to enter in a different system. The correct conditional structure is therefore “If you have a ticket, then you can enter the hall.” This expresses that a ticket alone is enough to ensure entry under the stated rule.

Option A:
Option A reverses the implication and would make having a ticket necessary rather than sufficient, changing the logical direction.

Option B:
Option B preserves the idea that a ticket is an adequate condition that guarantees the possibility of entry today.

Option C:
Option C contradicts the original statement by saying you can enter only without a ticket, which is the opposite of what is meant.

Option D:
Option D claims ticket possession is necessary but not sufficient, which again does not match the explicit statement about sufficiency.

Statements A, B and C present the standard relationships between necessary and sufficient conditions. A is correct because sufficiency ensures Q whenever P holds. B is true since necessity means Q cannot hold without P. C is correct as “necessary and sufficient” expresses logical equivalence. D is false; sufficiency does not generally reverse, and E is false because in “if P then Q”, P is sufficient and Q is necessary. Thus, A, B and C only are correct.

Option A:
Option A is incomplete because it omits C, and therefore does not explicitly mention the important notion of equivalence when a condition is both necessary and sufficient.

Option B:
Option B is incorrect because it includes E, which reverses the roles of P and Q in the implication, so this option accepts a false description of necessary and sufficient conditions.

Option C:
Option C is correct as it collects all three accurate conceptual definitions and excludes D and E, which misrepresent the direction and roles in implications.

Option D:
Option D is wrong since it adds D, which claims sufficiency reverses, and so includes a clear logical error alongside true statements, making the combination unacceptable.

A necessary condition is one without which a particular event cannot occur. Its absence guarantees that the event will not happen. However, its presence alone may not be enough to bring about the event because other conditions might also be required. Thus the description in the stem matches the concept of a necessary condition.

Option A:
Option A, sufficient, names a condition that by itself guarantees the occurrence of the event. A sufficient condition need not be required in every case. Therefore it does not fit the idea of something that must be present but may not be enough.

Option B:
Option B correctly identifies necessary as the label for conditions that are required but not independently adequate. If the necessary condition is missing, the event cannot occur. Hence this option is the best match for the stem.

Option C:
Option C, trivial, suggests an unimportant or insignificant factor and has no precise technical meaning in logical conditional analysis. A trivial condition might be present or absent without affecting the event. Thus trivial is not appropriate here.

Option D:
Option D, accidental, refers to something happening by chance and does not capture a stable logical dependency. An accidental factor is not necessarily required whenever the event occurs. Therefore accidental condition is not what the stem describes.

To say that p is necessary for q means that q cannot be true unless p is true. This is equivalent to saying that if p is absent, q must also be absent. Formally, this is symbolised as "if not p, then not q". Thus the conditional described in Option B captures the idea of necessity.

Option A:
Option A, "if p,then q", expresses that p is sufficient for q, since whenever p occurs, q follows. While related, sufficiency and necessity are different relations, and this conditional does not directly state that p is required for q.

Option B:
Option B is correct because "if not p,then not q" asserts that the failure of p guarantees the failure of q, which is exactly what a necessary condition demands. It is logically equivalent to the natural-language statement about necessity.

Option C:
Option C, "if q,then not p", says that whenever q is true, p must be false. This is the opposite of a necessity claim (which requires p when q holds) and would make p incompatible with q rather than required for it. Therefore it cannot represent "p is necessary for q".

Option D:
Option D, "if not q,then p", suggests that the absence of q guarantees the presence of p, a relation unrelated to standard necessity formulation. It neither captures necessity nor sufficiency as usually defined and so cannot be correct.

When we say X is necessary for Y, we mean that Y cannot occur without X. Here, the machine working (Y) cannot happen without electricity (X). In conditional form, that becomes: if the machine works, then electricity is present. This does not say that electricity alone is sufficient to make the machine work; it only says that working implies the presence of electricity.

Option A:
Option A correctly reverses the verbal statement into a conditional where the occurrence of machine functioning guarantees that electricity is available. It respects the asymmetry between necessity and sufficiency.

Option B:
Option B treats electricity as sufficient for the machine to work, which is stronger than what “necessary” states and may not be true if other conditions are required.

Option C:
Option C claims that a failure of the machine implies electricity is present, which is unrelated to the notion of electricity being required for proper functioning.

Option D:
Option D contradicts the original statement by saying the machine works even when the necessary condition, electricity, is absent.

Statements A, B, C, D and E are all correct descriptions of necessary and sufficient conditions, whereas F is false. Sufficiency requires that p’s truth guarantees q, and necessity means q is required for p. When a condition is both necessary and sufficient, the two statements are equivalent, and such cases do exist in logic and mathematics. Misunderstanding these notions can easily produce fallacies in exam questions, so E is also correct, while F contradicts the definition of a necessary condition by suggesting an impossible relation.

Option A:
Option A is incomplete because it omits E, failing to include the practically important warning about exam inferences. While A, B, C and D correctly outline theoretical relations, they do not address how confusion between them leads to mistakes in reasoning. Therefore A, B, C and D only does not contain all the correct statements provided.

Option B:
Option B is correct since it gathers all five true statements A, B, C, D and E and excludes F, which misrepresents necessity. It integrates the conceptual link between necessity, sufficiency and equivalence with the practical impact on inferential errors. Thus it accurately reflects the understanding expected in UGC NET Paper 1.

Option C:
Option C is incorrect because it leaves out D, which notes that a condition may indeed be both necessary and sufficient in certain contexts. Without D, the answer ignores an important nuance about how conditions can combine. The omission means this option does not fully represent the set of correct statements.

Option D:
Option D is wrong because it omits A, the basic link between sufficiency and conditional implication, and includes only B, C, D and E. Without A, the account of sufficient conditions is incomplete, even though the other four statements are true. Hence B, C, D and E only cannot be the right combination.

A necessary condition is one without which a particular event cannot occur. If the necessary condition is absent, the event is impossible. However, the necessary condition by itself may not be enough to bring about the event, as other conditions may also be required. This description is exactly what the stem presents, so it is a necessary condition.

Option A:
Option A is correct because the word necessary highlights the idea of requirement rather than guarantee. For example, oxygen is necessary for ordinary fire, but oxygen alone is not sufficient to produce fire. This illustrates the difference captured in the question.

Option B:
Option B, sufficient, refers to a condition that, when present, ensures the occurrence of an event by itself. A sufficient condition may not be required in every case, unlike a necessary one. Therefore sufficient condition does not match the focus on "must be present" in the stem.

Option C:
Option C, remote, suggests distance or weak connection and is not a standard technical expression in conditional logic. It does not tell us anything clear about necessity or sufficiency. Consequently remote is not the right answer.

Option D:
Option D, accidental, implies that something happens by chance and does not entail a stable conditional relation. An accidental factor may or may not be present without systematically affecting the event. Thus accidental condition does not fit the description.

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 necessary condition is one without which a given event or property cannot occur. If the necessary condition is absent, the event is impossible. However, simply having the necessary condition may not be enough to bring about the event because additional conditions might also be required. Thus the condition described in the stem is a necessary condition.

Option A:
Option A, sufficient, would mean that the condition by itself is enough to produce the event whenever it occurs. This emphasises guarantee rather than requirement, and so does not fit the stem’s description.

Option B:
Option B, causal, indicates that a factor plays some role in producing an effect, but not every cause is necessary and not every necessary condition is a direct cause. The term is therefore too vague for the precise logical relation required.

Option C:
Option C is correct because necessity focuses on what must hold whenever the event occurs. For instance, having oxygen is necessary for ordinary fire, even though oxygen alone cannot start a fire without fuel and ignition. This illustrates the idea that presence is required but not by itself sufficient.

Option D:
Option D, random, connotes lack of systematic relation and is the opposite of being required. A random factor is neither necessary nor reliably connected to the event.

Saying that p is necessary for q means that q cannot occur without p. This can be formally expressed as “if not p, then not q”. The two formulations always share the same truth conditions. Therefore they stand in a relation of logical equivalence.

Option A:
Option A, contrariety, concerns pairs of propositions that cannot both be true but may both be false. It does not capture the idea that two statements always have matching truth values. Hence contrariety is not the correct answer.

Option B:
Option B correctly identifies equivalence as the relation where two statements are true and false in exactly the same circumstances. The natural-language claim about necessity and the conditional “if not p, then not q” illustrate this. Thus equivalence is the best choice.

Option C:
Option C, subalternation, relates universal and particular propositions in the traditional square of opposition. It does not describe a mutual sameness of truth conditions. Therefore subalternation is not appropriate here.

Option D:
Option D, independence, refers to propositions whose truth values do not systematically constrain each other. This is the opposite of equivalence. Consequently independence cannot be the correct answer.

Statements A, B, C, D and E correctly characterise material implication and the distinction between necessary and sufficient conditions, while F is false. “If p then q” is indeed false only when p is true and q is false, and necessary conditions are those without which an outcome cannot obtain. Sufficient conditions guarantee an outcome when they occur, and confusing the two leads to errors like affirming the consequent. In the rain example, rain is treated as sufficient for wet ground, though not necessary because there may be other causes. Statement F reverses the relation between square and rectangle, since being a square is sufficient but not necessary for being a rectangle. Hence A, B, C, D and E only is the correct combination.

Option A:
Option A is correct because it includes all five accurate statements and excludes F, which mislabels the necessity relation between square and rectangle. It reflects standard logical semantics and familiar examples used in reasoning questions. Thus this option represents the complete and correct set of statements.

Option B:
Option B is incorrect since it adds F to the otherwise correct set, thereby endorsing a false description of the relationship between squares and rectangles. Squares meet the definition of rectangles, so being a rectangle is necessary for being a square, not the other way round. Including F therefore makes this option unsound.

Option C:
Option C is wrong because it omits B, leaving out the explicit definition of a necessary condition. Without B, the account of conditionals and conditions is incomplete, even though A, C, D and E are true. Therefore A, C, D and E only cannot be chosen.

Option D:
Option D is incorrect because it leaves out A and includes F, thereby ignoring the truth condition of material implication and accepting a mistaken example. This combination does not accurately represent the full set of correct statements about conditionals.