Let U = {x ∈ Z | −3 ≤ x ≤ 4} and A = {x ∈ U | x² < 4}. How many elements are in the complement A′ of A with respect to U?
Advertisement
Answer and explanation
Correct answer: 5
Use the complement-counting principle |A′| = |U| − |A|. The integers from −3 through 4 are U = {−3, −2, −1, 0, 1, 2, 3, 4}, so |U| = 8. The condition x² < 4 is equivalent to −2 < x < 2, giving A = {−1, 0, 1} and |A| = 3. Therefore |A′| = 8 − 3 = 5, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Use the complement-counting principle |A′| = |U| − |A|. The integers from −3 through 4 are U = {−3, −2, −1, 0, 1, 2, 3, 4}, so |U| = 8. The condition x² < 4 is equivalent to −2 < x < 2, giving A = {−1, 0, 1} and |A| = 3. Therefore |A′| = 8 − 3 = 5, so 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.
Advertisement