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MHT CET202416 May 2024Morning ShiftMathematicsSets and RelationsActual

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?

Options

  1. AThere is a rational number x ~S such that x 0 .
  2. BThere is no rational number x ~S such that x 0 .
  3. CEvery rational number x ~S satisfies x 0 .
  4. Dx ~S and x 0 x is not a rational number.

Correct answer

C. Every rational number x ~S satisfies x 0 .

Step-by-step solution

aligned & Given statement is & & x ~S , such that x 0 & ( x ~S , such that x 0) & x ~S , x 0 aligned i.e., Every rational number x S satisfies x 0 .

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