UGC NET Questions (Paper – 1)

Statements A, C and D give standard facts about quantifiers. A correctly identifies “for all n” as a universal quantifier. C is true because the negation of a universal statement is an existential statement with the predicate negated. D is also correct since negating an existential claim yields a universal statement with negated predicate. B is false because no natural number squared equals 2, and E is false because not all natural numbers are even. Therefore A, C and D only are correct.

Option A:
Option A is correct as it lists all the true statements: it recognises the universal quantification in A and the standard negation rules in C and D, while properly excluding B and E, which misstate facts about ℕ.

Option B:
Option B is incomplete since it omits D, ignoring the second important pattern for negating an existential statement. It therefore does not capture the full set of correct statements here.

Option C:
Option C is wrong as it drops A and includes only C and D, failing to mention the basic identification of a universal quantifier in statement A.

Option D:
Option D is incorrect because it adds E, which incorrectly claims that every natural number is even, so the combination contains a false universal statement.

This option is correct because the logical negation of a universal statement "All S are P" is an existential statement "Some S are not P." Here, "All students are punctual" negates to "Some students are not punctual." Thus, the correct word to fill the blank is "Some."

Option A:
Saying "No students are not punctual" would mean that every student is punctual, which actually restates the original universal claim in a different form. It does not express the negation. Therefore, this option is incorrect.

Option B:
The word "Most" suggests that a large majority of students are not punctual, which is stronger than merely saying at least one is not punctual. Negation in logic only needs one counterexample, so "most" is not the precise logical opposite of "all."

Option C:
The correct negation of a universal statement is existential, and "some" expresses the existence of at least one counterexample. Saying "Some students are not punctual" states that there is at least one student who fails the property, which contradicts the claim that all are punctual. Thus, this option correctly reflects the logical negation.

Option D:
Saying "Exactly two" students are not punctual again specifies a particular number of exceptions. Logical negation, however, only requires at least one exception and does not fix the number. Hence, this option is not the standard negation.