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+17 votes
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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:        

  • $G(x): x$ 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. $\forall x((G(x) \vee S(x)) \implies P(x))$
asked in Mathematical Logic by Veteran (14.6k points)
edited by | 889 views

3 Answers

+32 votes
Best answer

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).

 

answered by Loyal (4.1k points)
edited by
well , if we think about it an item can be both gold and silver at the same time BUT here in this context an item cant be gold and silver at same time because here gold & silver items are disjoint sets ... it's something we have to understand from the question
Yes "and" word is confusiing and leading to wrong answer. Ornament can not be both Gold and Silver at same time.
+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).
answered by Boss (7.5k points)
+2 votes

Option D this is just Same as lion and tiger question https://gateoverflow.in/989/gate2006-26 

answered by Boss (9.5k points)


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