Question

The negation of 'For every real number x, `x^2 ≥ 0`' is ______ 

Options

• For every real number x, x² ≤ 0

• For every real number x, x² < 0

• There exists a real number x, such that x² ≥ 0

• There exists a real number x, such that x² < 0

Answer 1

The negation of 'For every real number x, `x^2 ≥ 0`' is There exists a real number x, such that x² < 0.

Explanation:

The given statement is '∀ x ∈ R, x² ≥ 0' 

∼[∀ x ∈ R, x² ≥ 0] 

≡ ∃ x ∈ R, such that x² < 0

i.e., there exists a real number x, such that x² < 0.