Negation of a statement 'If $\forall x, x$ is a complex number then $x^2<0$ ' is

Negation of a statement 'If $\forall x, x$ is a complex number then $x^2<0$ ' is
  1. $\exists x, x$ is not a complex number and $x^2 \geq 0$
  2. $\exists x, x$ is not a complex number and $x^2<0$
  3. $\forall x, x$ is not a complex number and $x^2 \geq 0$
  4. $\forall \mathrm{x}, \mathrm{x}$ is not a complex number and $\mathrm{x}^2<0$

Solution

$\because$ Negation of 'if $p$ then $q$ ' is ' $p$ and not q'. Hence the required negation is $\forall x, x$ is a complex number and $x^2 \geq 0$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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