If U = {1, 2, ..., 22}, A = {x : x ∈ U, x is even}, and B = {x : x ∈ U, x is a perfect square}, what is (A ∩ B)'?
Answer and explanation
Correct answer: {1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22}
The perfect squares in U are 1, 4, 9, and 16. The even perfect squares, which belong to both A and B, are therefore A ∩ B = {4, 16}. The complement is taken within U, so remove 4 and 16 from {1, 2, ..., 22}. The remaining 20 elements are exactly the set listed in option A. Option B is the intersection itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22}
Why is this the correct answer?
The perfect squares in U are 1, 4, 9, and 16. The even perfect squares, which belong to both A and B, are therefore A ∩ B = {4, 16}. The complement is taken within U, so remove 4 and 16 from {1, 2, ..., 22}. The remaining 20 elements are exactly the set listed in option A. Option B is the intersection itself, not its complement.
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.
