If the universal set is U = {1, 2, 3, ..., 25} and A = {x ∈ U : x is a perfect square}, how many elements does Aᶜ contain?
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Answer and explanation
Correct answer: 20
The perfect squares in U from 1 through 25 are 1, 4, 9, 16, and 25. Thus A has 5 elements. The complement Aᶜ consists of every element of U that is not a perfect square. Because U has 25 elements, n(Aᶜ) = n(U) − n(A) = 25 − 5 = 20. Hence, option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The perfect squares in U from 1 through 25 are 1, 4, 9, 16, and 25. Thus A has 5 elements. The complement Aᶜ consists of every element of U that is not a perfect square. Because U has 25 elements, n(Aᶜ) = n(U) − n(A) = 25 − 5 = 20. Hence, option A is the only correct answer.
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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