Find the negation of the statement "No square of a real number is less than zero".

Question

Find the negation of the statement "No square of a real number is less than zero". (A) For every real number a,a2 is non-negative (B) ∀ a∈ R, a2≥ 0 (C) There exists a real number greater than 0 (D) There exists a real number less than 0

Tardigrade Admin · Accepted Answer

Square of a real number is always non-negative. Hence its negation will be: there exists a real number less than 0

Q. Find the negation of the statement "No square of a real number is less than zero".

For every real number $a, a^{2}$ is non-negative

$\forall a \in R, a^{2} \geq 0$

There exists a real number greater than $0$

There exists a real number less than $0$

Square of a real number is always non-negative.
Hence its negation will be: there exists a real number less than $0$

Q. Find the negation of the statement "No square of a real number is less than zero".

For every real number a,a2 is non-negative

∀a∈R,a2≥0

There exists a real number greater than 0