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Q.

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

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a

x  ∈  S  and x  ≤ 0⇒x  is not rational.

b

There is a rational number x  ∈  S  such that x>0

c

There is no rational number x  ∈  S  such that x≤0

d

Every rational number x  ∈  S  satisfies x≤0

answer is D.

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Detailed Solution

P:  there is a  rational number x∈S  such that x>0 ∼P:  every rational number x∈S  satisfies x≤0
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