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Question: Answered & Verified by Expert
The negation of the statement, $\exists x \in A$ such that $x+5>8$ is
MathematicsMathematical ReasoningMHT CETMHT CET 2020 (12 Oct Shift 2)
Options:
  • A $\forall x \in A, \quad x+5 \geq 8$
  • B $\forall x \in A, \quad x+5 \leq 8$
  • C $\forall x \in A, \quad x+5>8$
  • D $\exists x \in A$ such that $x+5 < 8$
Solution:
1037 Upvotes Verified Answer
The correct answer is: $\forall x \in A, \quad x+5 \leq 8$
While doing negation we replace $\exists$ by $\forall$ and $>$ by $\leq$.
So required statement is $\forall \mathrm{x} \in \mathrm{A}$ such that $\mathrm{x}+5 \leq 8$

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