If U = ℝ and A = {x ∈ ℝ : x ≠ −2 and x ≠ 5}, what is A′?
Answer and explanation
Correct answer: {−2, 5}
The universal set is the set of all real numbers. Set A contains every real number except −2 and 5, because those two values are explicitly excluded by the conditions. Therefore, the complement A′, which contains elements of U that are not in A, consists exactly of the two excluded real numbers: A′ = {−2, 5}.
Frequently asked questions
What is the correct answer to this question?
{−2, 5}
Why is this the correct answer?
The universal set is the set of all real numbers. Set A contains every real number except −2 and 5, because those two values are explicitly excluded by the conditions. Therefore, the complement A′, which contains elements of U that are not in A, consists exactly of the two excluded real numbers: A′ = {−2, 5}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
