Solving Lesson 6 Page 8 Math Workbook 10 – Kite>

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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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