Which of the following is an empty set?

Question

Accepted Answer

Let's check the options: (A) $\{x : x^2 - 2 = 0 	ext{ and } x 	ext{ is rational}\}$ has no rational solution since $\sqrt{2}$ is irrational. (B) $\{x : x^2 = 4 	ext{ and } x 	ext{ is even}\}$ has solution $x = \pm 2$. (C) $\{x : x 	ext{ is a real number and } x > x\}$ is always false. Wait, option A gives an empty set because $x^2 = 2 \implies x = \pm\sqrt{2}$, which are not rational numbers.

Sets

❓ Sibling Questions in this Chapter