Quantifiers and categorical statements – UGC NET Question

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.