Mathematical Reasoning: Which of the following is the negation of the statement ``for all… | JEE Main 2021

JEE Main 2021 (Online) 27th July Evening ShiftQuestion 1

Which of the following is the negation of the statement ``for all $M>0$, there exists $x\in S$ such that $x\ge M$'' ?

Mathematical Reasoning

there exists $M>0$, there exists $x\in S$ such that $x<M$there exists $M>0$, there exists $x\in S$ such that $x\ge M$there exists $M>0$, such that $x<M$ for all $x\in S$✓ Correct answerthere exists $M>0$, such that $x\ge M$ for all $x\in S$

Solution

$\sim(\forall M\,\exists x: x\ge M)=\exists M\,\forall x: x<M$.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2021 (Online) 27th July Evening Shift)

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