## Solving Lesson 6 Page 8 Math Workbook 10 – Kite>

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.