GATE | GATE-CS-2009 | Question 23

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))


Answer: (D)

Explanation:  

=> This statement can be expressed as
=> For all X, x can be either gold or silver then the ornament X is precious
=> For all X, (G(X) v S(x)) => P(X).

This solution is contributed by Anil Saikrishna Devarasetty .


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