Verified Solution • 2025–26 Session moderate

QJEEM21Ma1f37: JEE Main 2021 Mathematics - Class 11 JEEM21Ma1f37 Solution: Which of the following is the negation of the statement "for…

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

Multiple Choice Options

  • A there exists M > 0, such that x < M for all x∈S
  • B there exists M > 0, there exists x∈S such that x ≥ M
  • C there exists M > 0, there exists x∈S such that x < M
  • D there exists M > 0, such that x ≥ M for all x∈S

Step-by-Step Verified 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 exists' is 'for all'.

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