Which of the following is an empty set? - Mathematics MCQ Mathematics Mock Test - 6 2026 | ExamTest.live | ExamTest.live

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Which of the following is an empty set?

A ${x : x \in Q, x^{2} - 1 = 0}$
B ${x : x \in Q, x^{2} - 9 = 0}$
C ${x : x \in Q, x^{2} - 4 = 0}$
D ${x : x \in Q, x^{2} + 1 = 0}$

Solution & Step-by-step Explanation

A set is empty if no element satisfies the condition. x^{2} - 1 = 0 ⟹ x = \pm 1 (Rational). Not empty. x^{2} - 9 = 0 ⟹ x = \pm 3 (Rational). Not empty. x^{2} - 4 = 0 ⟹ x = \pm 2 (Rational). Not empty. x^{2} + 1 = 0 ⟹ x^{2} = - 1 ⟹ x = \pm i .Since \pm i are imaginary numbers and not rational (Q), no rational number satisfies the equation. This is an empty set.

Practice this question

Try it yourself before checking the explanation above.

Which of the following is an empty set?

A

{x : x \in Q, x^{2} - 1 = 0}

B

{x : x \in Q, x^{2} - 9 = 0}

C

{x : x \in Q, x^{2} - 4 = 0}

D

{x : x \in Q, x^{2} + 1 = 0}

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