UGC NET Questions (Paper – 1)

Statement C is wrong because the correct negation of “All X are Y” is “Some X are not Y”, not “No X are Y”; denying a universal requires asserting the existence of at least one counterexample, not universal negation. Statements A and B correctly identify universal and existential quantifications, D correctly notes that the negation of “Some X are Y” is “No X are Y”, and E accurately explains the meaning of “Some X are not Y”. Therefore, the only incorrect statement is C, so the option that lists C only is correct.

Option A:
Option A is incorrect because it treats A and C as wrong together, even though A correctly states that “All teachers are researchers” is universally quantified. By marking A as wrong, this option misrepresents basic quantifier classification.

Option B:
Option B is wrong since it pairs C with D as wrong, despite D correctly expressing the negation of an existential statement. Including D among wrong statements contradicts standard quantifier negation rules.

Option C:
Option C is incorrect as it groups B, C and E as wrong, even though B and E correctly explain existential quantification and the meaning of “Some X are not Y”. This option therefore rejects true statements along with the single false one.

Option D:
Option D is correct because it isolates C as the only statement that misstates a quantifier negation, while implicitly affirming the accuracy of A, B, D and E. It preserves the canonical equivalences used in UGC NET logic questions.

From the first statement, we know that every square belongs to the set of rectangles. The second statement says that no rectangles belong to the set of circles, so the sets of rectangles and circles are disjoint. Since squares are a subset of rectangles, and rectangles do not overlap with circles, squares also cannot overlap with circles. Therefore, the conclusion that no squares are circles is logically valid.

Option A:
Option A, “Some squares are circles,” contradicts the second premise. If any square were also a circle, it would simultaneously be a rectangle and a circle, which is impossible when no rectangles are circles.

Option B:
Option B, “No squares are circles,” correctly applies the idea that if rectangles and circles are disjoint sets, then any subset of rectangles (such as squares) must also be disjoint from circles. Hence, no square can be a circle.

Option C:
Option C, “All circles are squares,” reverses and overextends the relationship. We are told only that all squares are rectangles, not that all circles are contained in the set of squares.

Option D:
Option D, “Some rectangles are circles,” is directly inconsistent with the second statement, which asserts that no rectangles are circles.

From “Some doctors are writers” and “All writers are researchers,” we know that there is at least one person who is both a doctor and a writer, and all writers fall within the class of researchers. Therefore, that doctor must also be a researcher. This supports the conclusion that some doctors are researchers. The same overlapping individual also lies in the intersection of doctors and researchers, so it is equally true that some researchers are doctors. Thus, both statements A and C follow.

Option A:
Option A correctly notes that at least one doctor must be a researcher, deriving this from the overlapping subset of doctor-writers being within researchers.

Option B:
Option B overgeneralises by claiming that every doctor is a researcher, which is not warranted by the premises.

Option C:
Option C correctly focuses on the researcher side and notes that some researchers are doctors, because the overlapping individuals are in the researcher class.

Option D:
Option D acknowledges that both perspectives on the same intersection are logically supported, whereas B is not.

The first premise places engineers inside the set of problem solvers, and the second places problem solvers inside the set of creative people. By transitivity of class inclusion, engineers are contained within the set of creative people. This yields the conclusion that all engineers are creative. The direction of inclusion is important: the statements do not claim that all creative people are engineers.

Option A:
Option A correctly follows the chain Engineers ⊆ Problem solvers ⊆ Creative, so Engineers ⊆ Creative. It respects the one-way inclusion implied by the premises.

Option B:
Option B reverses the relationship and claims that every creative person is an engineer, which is much stronger than what is given.

Option C:
Option C might be true in reality, but it is not logically forced by the premises, which say nothing about creative people who are not problem solvers.

Option D:
Option D contradicts the premises, because if all engineers are creative, it cannot be the case that no creative person is an engineer.

For an E-type universal negative proposition like "No S are P", simple conversion is valid and yields "No P are S". This new statement preserves both the quantity and quality of the original while exchanging subject and predicate. The two propositions express the same exclusion relation between the classes. Hence the correct converted form is "No P are S".

Option A:
Option A, "All P are S", changes both the quantity and the quality of the original statement. It asserts a universal affirmative rather than a universal negative and therefore cannot be logically equivalent to "No S are P".

Option B:
Option B, "Some P are S", asserts an existential particular affirmative that contradicts the universal exclusion in the original. It would claim overlapping membership where the original denies any overlap. Thus it is not a valid conversion.

Option C:
Option C is correct because the conversion of an E proposition simply reverses the positions of subject and predicate while maintaining "no" as the quantifier. This keeps the meaning that the two classes do not share any members, which is consistent with the original statement.

Option D:
Option D, "Some P are not S", changes the form to a particular negative and does not preserve the universal denial of overlap. It allows the possibility that some P are S, which conflicts with the original universal negative.

The first premise places all athletes inside the set of disciplined people, guaranteeing an overlap between those categories as long as athletes exist. Therefore, some disciplined people must be athletes. The second premise concerns a subset of disciplined people who lack punctuality but does not directly specify whether that subset includes athletes. Thus, we cannot infer anything specific about athletes’ punctuality, but we can affirm that some disciplined persons are athletes.

Option A:
Option A would require that some of the non-punctual disciplined people are athletes, which the premises do not guarantee.

Option B:
Option B goes further and claims that no athlete is punctual, which is unsupported.

Option C:
Option C makes the weaker and logically certain claim that at least one disciplined person is an athlete, which follows from “all athletes are disciplined” under the assumption that athletes exist.

Option D:
Option D introduces a statement about punctual people that is not addressed by the premises and so cannot be logically concluded.

Contraposition is an operation that takes a conditional or certain categorical propositions and transforms them by swapping subject and predicate while also negating each. For example, “If p, then q” becomes “If not q, then not p”, and these are logically equivalent. This method is often used in proofs because the contrapositive of a true conditional must also be true. Thus the inference described in the stem is contraposition.

Option A:
Option A, conversion, simply interchanges subject and predicate without negating them, as when “No S are P” is converted to “No P are S”. It does not include the additional step of negation that characterises contraposition.

Option B:
Option B, obversion, changes the quality of a proposition and replaces the predicate with its complement but does not interchange subject and predicate. It is a different immediate inference.

Option C:
Option C is correct because contraposition uniquely combines reversal of order with negation of both terms, yielding a statement equivalent to the original under classical logic for suitable forms. This fits the description given in the question.

Option D:
Option D, equipollence, is sometimes used to describe equivalence obtained by combining operations like obversion and conversion, but it is not the standard name for the specific transformation outlined in the stem.