Solving Lesson 4 Page 8 Math Workbook 10 – Kite>

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Topic

The negation of the statement “\(\exists x \in \mathbb{R},{x^2} – x + 1 < 0\)” is the proposition:

A. “\(\forall x \in \mathbb{R},{x^2} – x + 1 \ge 0\)”

B. “\(\forall x \in \mathbb{R},{x^2} – x + 1 < 0\)”

C. “\(\forall x \in \mathbb{R},{x^2} – x + 1 > 0\)”

D. “\(\exists x \in \mathbb{R},{x^2} – x + 1 \ge 0\)”

Solution method – See details

The negation of the clause “\(\exists x \in X,P(x)\)” is “\(\forall x \in X,\overline {P(x)} \)”

Detailed explanation

The negation of the clause “\(\exists x \in \mathbb{R},{x^2} – x + 1 < 0\)” is “\(\forall x \in \mathbb{R}, {x^2} – x + 1 \ge 0\)”

Choose A.

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