Let U = {x ∈ Z : −5 ≤ x ≤ 5} and A = {x ∈ U : |x| ≤ 2}. How many elements does the complement A′ relative to U contain?
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Answer and explanation
Correct answer: 6
The universal set U contains the integers −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, and 5, so |U| = 11. The condition |x| ≤ 2 gives A = {−2, −1, 0, 1, 2}, which has 5 elements. The complement relative to U therefore has |A′| = |U| − |A| = 11 − 5 = 6 elements. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The universal set U contains the integers −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, and 5, so |U| = 11. The condition |x| ≤ 2 gives A = {−2, −1, 0, 1, 2}, which has 5 elements. The complement relative to U therefore has |A′| = |U| − |A| = 11 − 5 = 6 elements. Hence option C is correct.
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.
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