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Let S be a non-empty subset of R. Consid...

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

A

There is a rational number `x in S` such that `x le 0`

B

There is no rational number `x in S` such that `x le 0`

C

Every rational number `x in S` satisfies `x le 0`

D

`x in S` and `x le 0 rArr x` is not rational

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The correct Answer is:
C
Given, P : There is rational number `x in S` such that `x gt 0`.
`~ P` : Every rational number `x in S` satisifies `x le 0` .
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATHEMATICAL LOGIC -MHT CET CORNER
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