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Which one of the following is the most appropriate logical formula to represent | Which one of the following is the most appropriate logical formula to represent | ||
| − | the statement? | + | the statement? |
| − | + | ||
| + | "Gold and silver ornaments are precious". | ||
| + | |||
The following notations are used: | 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) $\forall x((G(x) ∨ S(x)) \implies P(x))$''' | |
==={{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: | + | [[Category: Mathematical Logic questions from GATE]] |
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:
(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) ∀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))
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