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40 votes
40 votes

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
  1. $\forall x(P(x) \implies (G(x) \wedge S(x)))$
  2. $\forall x((G(x) \wedge S(x)) \implies P(x))$
  3. $\exists x((G(x) \wedge S(x)) \implies P(x))$
  4. $\forall x((G(x) \vee S(x)) \implies P(x))$
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8 Answers

Best answer
56 votes
56 votes

The statement could be translated as, if $x$ is either Gold or Silver, then it would be precious. Rather than,

If $x$ is both Gold and Silver, as an item cannot both Gold and silver at the same time.

Hence Ans is (D).

edited by
9 votes
9 votes

"Gold and silver ornaments are precious"

For all x, x can be either Gold or Silver ornament then the x is precious.

2 votes
2 votes
This statement can be expressed as => For all X, x can be either gold or silver then the ornament X is precious => For all X, (G(X) v S(x)) => P(X).
Answer:

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