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Question

If S be a non-empty subset of R. Consider the following statement P: There is a rational number xS such that x>0. Which of the following statements is the negation of statement P?


A

There is a rational number xS such that x0

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B

There is no rational number xS such that x0

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C

Every rational number xS such that x0

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D

xSandx0x is not rational

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Solution

The correct option is C

Every rational number xS such that x0


Finding the negation of statement P:

As per the given statement P, there is a rational number xS, so the negation of this part will be every rational number xS.

Let us focus on the second part that says x>0, so the negation of this will be x0.

Therefore, the negation of P or ~P will be every rational number xS such that x0..

Hence, the correct option is (C).


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