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Topic
The negation of the statement “\(\forall x \in \mathbb{R},{x^2} \ge 0\)” is the proposition:
A. “\(\exists x \in \mathbb{R},{x^2} \ge 0\)”
B. “\(\exists x \in \mathbb{R},{x^2} > 0\)”
C. “\(\exists x \in \mathbb{R},{x^2} \le 0\)”
D. “\(\exists x \in \mathbb{R},{x^2} < 0\)”
Solution method – See details
The negation of the clause “\(\forall x \in X,P(x)\)” is “\(\exists x \in X,\overline {P(x)} \)”
Detailed explanation
The negation of the clause “\(\forall x \in \mathbb{R},{x^2} \ge 0\)” is “\(\exists x \in \mathbb{R},{x^) 2} < 0\)”
Choose D.
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