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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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