The negation of the statement, $\exists x \in A$ such that $x+5>8$ is

The negation of the statement, $\exists x \in A$ such that $x+5>8$ is
  1. $\forall x \in A, \quad x+5 \geq 8$
  2. $\forall x \in A, \quad x+5 \leq 8$
  3. $\forall x \in A, \quad x+5>8$
  4. $\exists x \in A$ such that $x+5 < 8$

Solution

While doing negation we replace $\exists$ by $\forall$ and $>$ by $\leq$. So required statement is $\forall \mathrm{x} \in \mathrm{A}$ such that $\mathrm{x}+5 \leq 8$

Asked in: MHT CET 2020 (12 Oct Shift 2)

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