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JEE Main 202127 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
27 July
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2021 · 27 July · Evening Shift · Mathematics · Mathematical Reasoning

Which of the following is the negation of the statement "for all M...

Which of the following is the negation of the statement "for all M>0,M > 0, there exists x∈Sx \in S such that x \ge {M}^{' '} ?

Options

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

Correct answer

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

Step-by-step solution

P:P: for all M>0,M > 0, there exists x∈Sx \in S such that x≥Mx \ge M

 P:~ P: there exists M>0,M > 0, for all x∈Sx \in S such that x<mx < m

Negation of 'there exsits' is 'for all'.

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