JEE Main · MathematicsHard

$The negation of the statement 'For all real numbers x, if x^{2} > 0, then x > 0' is:$

A. $There exists a real number x such that x^{2} > 0 and x \leq 0 .$
B. $For all real numbers x, x^{2} > 0 and x \leq 0 .$
C. $There exists a real number x such that x^{2} \leq 0 and x > 0 .$
D. $For all real numbers x, if x^{2} > 0, then x \leq 0 .$

Show correct answer & step-by-step solution

Correct answer: A — $There exists a real number x such that x^{2} > 0 and x \leq 0 .$

Solution

The negation of \forall x, P (x) ⟹ Q (x) is \exists x, P (x) \land \neg Q (x) . Here, P (x) is x^{2} > 0 and Q (x) is x > 0, so the negation is x^{2} > 0 and x \leq 0 .

Attempt this question & track your score

Sign up free to answer, get instant scoring, and let SolveGini track which Mathematics topics you need to revise.

Attempt & Track Free →

More Mathematical Reasoning practice questions

View all Mathematical Reasoning questions →