GATE2009 q23 Revision as of 12:57, 14 July 2014 by Arjun Suresh (talk | contribs) (Created page with "Which one of the following is the most appropriate logical formula to represent the statement? $``$Gold and silver ornaments are precious$''$. <br> The following notatio...") (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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) ∀x(P(x) → (G(x) ∧ S(x)))   (B) ∀x((G(x) ∧ S(x)) → P(x))
(C) ∃;x((G(x) ∧ S(x)) → P(x))
(D) ∀x((G(x) ∨ S(x)) → P(x))

Solution by Happy Mittal

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.

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