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

(C) $\exists x((G(x) \wedge S(x)) \implies P(x))$

(D) $\forall x((G(x) ∨ S(x)) \implies P(x))$

Solution by Happy Mittal[edit]

Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious.

So, $\forall x((G(x) ∨ S(x)) \implies P(x))$ is correct logical formula.