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Question: Answered & Verified by Expert
Negation of the statement $\forall \mathrm{x} \in \mathrm{R}, \mathrm{x}^2+1=0$ is
MathematicsMathematical ReasoningMHT CETMHT CET 2021 (21 Sep Shift 1)
Options:
  • A $\exists x \in R$ such that $x^2+1 < 0$
  • B $\exists x \in R$ such that $x^2+1 \leq 0$
  • C $\exists x \in R$ such that $x^2+1 \neq 0$
  • D $\exists \mathrm{x} \in \mathrm{R}$ such that $\mathrm{x}^2+1=0$
Solution:
2458 Upvotes Verified Answer
The correct answer is: $\exists x \in R$ such that $x^2+1 \neq 0$
$$
\text { Negation of }\left(\forall x \in R, x^2+1=0\right) \text { is } \exists x \in R \text {, such that } x^2+1 \neq 0
$$

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