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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 following statement:
P: There is a rational number `x inS` such that `xgt0`.
Which of the following statements is the negation of the statement P?

A

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

B

There is rational number `x in S` such that `xle0`.

C

There is no rational number `x in S` such that `xle0`.

D

Every rational number `x in S` satisfies `xle0`

Text Solution

Verified by Experts

The correct Answer is:
D
P: There is a rational bumber `x in S` such that `x gt0`
`~p `: Every rational number `x in S` satisfies `xle0`
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