If the universal set is U = {1, 2, ..., 100} and A = {x ∈ U : x is a perfect square}, what is the value of |A′|?
Answer and explanation
Correct answer: 90
The universal set has |U| = 100 elements. The perfect squares in this range are 1², 2², 3², ..., 10², ending at 100, so A contains exactly 10 elements. The complement contains every member of U that is not a perfect square. Therefore |A'| = |U| − |A| = 100 − 10 = 90. Option B is correct. Counting 0 or a square above 100 would be inappropriate because neither belongs to the stated universal set.
Frequently asked questions
What is the correct answer to this question?
90
Why is this the correct answer?
The universal set has |U| = 100 elements. The perfect squares in this range are 1², 2², 3², ..., 10², ending at 100, so A contains exactly 10 elements. The complement contains every member of U that is not a perfect square. Therefore |A'| = |U| − |A| = 100 − 10 = 90. Option B is correct. Counting 0 or a square above 100 would be inappropriate because neither belongs to the stated universal set.
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.
