If U = {1, 2, ..., 25}, A = {x : x is odd} and B = {x : x is a perfect square}, what is |A' ∩ B|?
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Answer and explanation
Correct answer: 2
The universal set contains the integers from 1 through 25. Since A is the set of odd numbers, its complement A' within U is the set of even numbers. The perfect squares in U are {1, 4, 9, 16, 25}. Among them, the even squares are 4 and 16. Therefore, A' ∩ B = {4, 16}, and its cardinality is 2.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The universal set contains the integers from 1 through 25. Since A is the set of odd numbers, its complement A' within U is the set of even numbers. The perfect squares in U are {1, 4, 9, 16, 25}. Among them, the even squares are 4 and 16. Therefore, A' ∩ B = {4, 16}, and its cardinality is 2.
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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