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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. $\forall x((G(x) \vee S(x)) \implies P(x))$
edited | 1.4k views
+1
How can we know that an ornament cannot be made of gold and silver both. We see ornaments that have both gold in some parts and silver in other parts. We cannot judge the ornaments with this given information ryt? Moreover then what will be the meaning of this " gold or silver ornaments are precious"?

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
+14
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
+5
Yes "and" word is confusiing and leading to wrong answer. Ornament can not be both Gold and Silver at same time.

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

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).

"Gold and silver ornaments are precious"

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

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