JEE Main · MathematicsEasy

$What is the negation of the statement: \forall x \in R, x^{2} \geq 0 ?$

A. $\forall x \in R, x^{2} < 0$
B. $\exists x \in R, x^{2} < 0$
C. $\exists x \in R, x^{2} > 0$
D. $\forall x \in R, x^{2} \neq = 0$

Show correct answer & step-by-step solution

Correct answer: B — $\exists x \in R, x^{2} < 0$

Solution

$The given statement is \forall x \in R, x^{2} \geq 0 .$
$The negation of \forall x is \exists x .$
$The negation of the condition x^{2} \geq 0 is x^{2} < 0 .$
$Combining these, the negation is \exists x \in R, x^{2} < 0 .$
$Hence the answer is (B).$

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