UGC NET Questions (Paper – 1)

The phrase "for every real number x" indicates that the statement is being made about all real numbers without exception. In logic, this is expressed using the universal quantifier, typically denoted by ∀. It asserts that the property x² ≥ 0 holds for each element in the domain of discourse. Therefore, the statement employs the universal quantifier.

Option A:
Universal quantifier is correct because it captures the idea of generality over an entire set. In symbolic form, the statement would be written as ∀x ∈ ℝ, x² ≥ 0. This form is frequently used in mathematical proofs and theoretical reasoning in aptitude tests and higher mathematics.

Option B:
An existential quantifier is used when we assert that there exists at least one element in the domain with a given property, usually expressed as "there exists." The given statement, however, does not say "there exists some x" but "for every x," making the existential quantifier inappropriate.

Option C:
Negative quantifier is not a standard term in formal logic. Negation can apply to quantified statements, but the main quantifiers are universal and existential. Since the question refers to a well-defined quantifier symbol, this option does not match known terminology.

Option D:
Dual quantifier is not a commonly used name in basic logic courses or in the UGC NET syllabus. While universal and existential quantifiers can be viewed as duals in a theoretical sense, the specific statement here plainly uses the universal form. Thus, this is not the correct label.