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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? $``$Gold and silver ornaments are precious$''$. | the statement? $``$Gold and silver ornaments are precious$''$. | ||
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The following notations are used: | The following notations are used: | ||
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| − | G(x): x is a gold ornament | + | $G(x): x$ is a gold ornament |
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| − | S(x): x is a silver ornament | + | $S(x): x$ is a silver ornament |
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| − | P(x): x is precious | + | $P(x): x$ is precious |
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| − | + | (A) $\forall;x(P(x) \rarr (G(x) \wedge S(x)))$ | |
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<b>(B) </b>∀x((G(x) ∧ S(x)) → P(x)) | <b>(B) </b>∀x((G(x) ∧ S(x)) → P(x)) | ||
<br> | <br> | ||
<b>(C) </b>∃;x((G(x) ∧ S(x)) → P(x)) | <b>(C) </b>∃;x((G(x) ∧ S(x)) → P(x)) | ||
<br> | <br> | ||
| − | + | (D) </b>∀x((G(x) ∨ S(x)) → P(x)) | |
==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ||
<b>Sol : </b> Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious. | <b>Sol : </b> Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious. | ||
Which one of the following is the most appropriate logical formula to represent the statement? $``$Gold and silver ornaments are precious$$.
The following notations are used:
$G(x): x$ is a gold ornament
$S(x): x$ is a silver ornament
$P(x): x$ is precious
(A) $\forall;x(P(x) \rarr (G(x) \wedge S(x)))$
(B) ∀x((G(x) ∧ S(x)) → P(x))
(C) ∃;x((G(x) ∧ S(x)) → P(x))
(D) </b>∀x((G(x) ∨ S(x)) → P(x))
Sol : Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious.
So ∀x((G(x) ∨ S(x)) → P(x)) is correct logical formula, and therefore option (D) is correct.
Which one of the following is the most appropriate logical formula to represent
the statement? $``$Gold and silver ornaments are precious$$.
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