Difference between revisions of "GATE2009 q23"

Revision as of 14:11, 14 July 2014

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.

@@ Line 10: / Line 10: @@
 		$P(x): x$ is precious
-		(A) $\forall;x(P(x) \implies (G(x) \wedge S(x)))$
+		(A) $\forall x(P(x) \implies (G(x) \wedge S(x)))$
-		<b>(B) </b>&forall;x((G(x) &and; S(x)) &rarr; P(x))
+		(B) $\forall x((G(x) \wedge S(x)) \implies P(x))$
-		<br>
-		<b>(C) </b>&exist;;x((G(x) &and; S(x)) &rarr; P(x))
+		(C) $\exists x((G(x) \wedge S(x)) \implies P(x))$
-		<br>
-		(D) </b>&forall;x((G(x) &or; S(x)) &rarr; P(x))
+		'''(D) $\forall x((G(x) &or; S(x)) \implies P(x))$'''
 ==={{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.
+Basically statement is saying that for every thing, if it is a Gold ornament or a silver ornament, then it is precious.
-		<br>
-		So &forall;x((G(x) &or; S(x)) &rarr; P(x)) is correct logical formula, and therefore option <b>(D)</b> is correct.
+		So, $\forall x((G(x) &or; S(x)) \implies P(x))$ is correct logical formula.
 {{Template:FBD}}
 [[Category: GATE2009]]
 [[Category: Logical Inference questions]]