Arjun Suresh (talk | contribs) |
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$P(x): x$ is precious | $P(x): x$ is precious | ||
| − | (A) $\forall | + | (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) | + | '''(D) $\forall x((G(x) ∨ S(x)) \implies P(x))$''' |
==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ||
| − | + | Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious. | |
| − | + | ||
| − | So | + | So, $\forall x((G(x) ∨ S(x)) \implies P(x))$ is correct logical formula. |
{{Template:FBD}} | {{Template:FBD}} | ||
[[Category: GATE2009]] | [[Category: GATE2009]] | ||
[[Category: Logical Inference questions]] | [[Category: Logical Inference questions]] | ||
Which one of the following is the most appropriate logical formula to represent the statement? $``$Gold and silver ornaments are precious$$.
The following notations are used:
$G(x): x$ is a gold ornament
$S(x): x$ is a silver ornament
$P(x): x$ is precious
(A) $\forall x(P(x) \implies (G(x) \wedge S(x)))$
(B) $\forall x((G(x) \wedge S(x)) \implies P(x))$
(C) $\exists x((G(x) \wedge S(x)) \implies P(x))$
(D) $\forall x((G(x) ∨ S(x)) \implies P(x))$
Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious.
So, $\forall x((G(x) ∨ S(x)) \implies P(x))$ is correct logical formula.
Which one of the following is the most appropriate logical formula to represent the statement? $``$Gold and silver ornaments are precious$$.
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))
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.
GATECSE