GATE 2012 CS (CS1) – Question 23

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 1 mark · Multiple choice

Translate “Some real numbers are rational” into logic.

$\exists x(real(x)\lor rational(x))$
$\forall x(real(x)\to rational(x))$
$\exists x(real(x)\land rational(x))$
$\exists x(rational(x)\to real(x))$

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Show answer and explanation

Correct answer: (C) $\exists x(real(x)\land rational(x))$

Explanation

“Some” supplies an existential quantifier, and the witness must satisfy both being real and being rational. Therefore ∃x(real(x)∧rational(x)), C. Disjunction or implication would allow witnesses not satisfying both properties.

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