View source for GATE2009 q23 ← GATE2009 q23

Which one of the following is the most appropriate logical formula to represent the statement? $``$Gold and silver ornaments are precious$$.

The following notations are used:

$G(x): x$ is a gold ornament

$S(x): x$ is a silver ornament

$P(x): x$ is precious

(A) $\forall;x(P(x) \implies (G(x) \wedge S(x)))$

(B) ∀x((G(x) ∧ S(x)) → P(x))
(C) ∃;x((G(x) ∧ S(x)) → P(x))
(D) </b>∀x((G(x) ∨ S(x)) → P(x))

Solution by Happy Mittal[edit]

Sol : Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious.
So ∀x((G(x) ∨ S(x)) → P(x)) is correct logical formula, and therefore option (D) is correct.