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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".
 
 
 
The following notations are used:
 
The following notations are used:

Revision as of 14:28, 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) $\forall x((G(x) ∨ S(x)) \implies P(x))$

Solution by Happy Mittal

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.



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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) $\forall x((G(x) ∨ S(x)) \implies P(x))$

Solution by Happy Mittal[edit]

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.



blog comments powered by Disqus