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JEE Main202127 Jul 2021Evening ShiftMathematicsMathematical ReasoningActual

Which of the following is the negation of the statement "for all M > 0 , there exists x ∈ S such that x ≥ M ' ' ?

Options

  1. Athere exists M > 0 , such that x < M for all x ∈ S
  2. Bthere exists M > 0 , there exists x ∈ S such that x ≥ M
  3. Cthere exists M > 0 , there exists x ∈ S such that x < M
  4. Dthere exists M > 0 such that x ≥ M for all x ∈ S

Correct answer

A. there exists M > 0 , such that x < M for all x ∈ S

Step-by-step solution

P : for all M > 0 , there exists x ∈ S such that x ≥ M ~ P : there exists M > 0 , for all x ∈ S such that x < m Negation of 'there exsits' is 'for all'.

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