Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

Given the proposition ¬P: ∀x∈R, $x^2>0$ , then the proposition P is

Pick one

Solution

Since the original proposition is a universal proposition, the negation of the original proposition is an existential proposition.
Therefore, the negation of the proposition ¬P: ∀x∈R, $x^2>0$ , is: P: ∃x∈R, $x^2≤0$ .
Hence, the correct choice is $\boxed{C}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.