GATE CSE 2009 | Question: 23

Question

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. $\forall x((G(x) \vee S(x)) \implies P(x))$

Comments

Note : X cannot be both gold and silver at same time

           X cannot be both lion and tiger at same time

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Very easy and Explain every option Meaning 

https://gateoverflow.in/800/gate-cse-2009-question-23?show=537665#a537665

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At Timestamp -> https://youtu.be/s41PLmHGf08?list=PLIPZ2_p3RNHidhFvyKH4U_VE1rFAyvG8U&t=2177

 

Answer 1

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).

Comments

These logic are more confusing. Sometimes propositions doesn't convey any real meaning if we try to solve them according to simple english sentence then we might do it wrong.

But here we have to use intuition.. /

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note:And will come when combination of both gives the result and Or will come when anyone enough gives the result

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This question try to confuse you with keyword "and" but keep in mind that two objects can't same.

So a very beautiful question.

Answer 2

By default when no quantifier words is present then it is assumed that it is “All”

Option D is correct.

Answer 3

"Gold and silver ornaments are precious"

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

Answer 4

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

Answer 5

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 6

Option D

First thing that we need to keep in mind is to decide the domain. Since, they did'nt specified what x is,  we will take x as all ornaments in the universe.

Second thing, Here in the question the word and is misleading & it does'nt mean that the ornament will be Gold & Silver. It can either be Gold or Silver.

Third is correct choice of quantifier.

if we use existential quantifier, it will mean that at least one Gold or Silver ornament is precious, which is not what the statement is saying. if the ornament is Gold or Silver then it will be precious.(all Gold or Silver ornament are precious). So we have to use universal quantifier.