Negation of the statement $\forall \mathrm{x} \in \mathrm{R}, \mathrm{x}^2+1=0$ is

Negation of the statement $\forall \mathrm{x} \in \mathrm{R}, \mathrm{x}^2+1=0$ is
  1. $\exists x \in R$ such that $x^2+1 < 0$
  2. $\exists x \in R$ such that $x^2+1 \leq 0$
  3. $\exists x \in R$ such that $x^2+1 \neq 0$
  4. $\exists \mathrm{x} \in \mathrm{R}$ such that $\mathrm{x}^2+1=0$

Solution

$\text { Negation of }\left(\forall x \in R, x^2+1=0\right) \text { is } \exists x \in R \text {, such that } x^2+1 \neq 0$

Asked in: MHT CET 2021 (21 Sep Shift 1)

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