If the universal set is U = {1, 2, ..., 30} and A = {x : x ∈ U and the last digit of x is 0 or 5}, what is n(A′)?
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Answer and explanation
Correct answer: 24
The members of A whose last digit is 0 or 5 are 5, 10, 15, 20, 25, and 30, so n(A) = 6. The universal set contains 30 elements. Since A′ contains all elements of U not in A, the complement formula gives n(A′) = n(U) − n(A) = 30 − 6 = 24. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The members of A whose last digit is 0 or 5 are 5, 10, 15, 20, 25, and 30, so n(A) = 6. The universal set contains 30 elements. Since A′ contains all elements of U not in A, the complement formula gives n(A′) = n(U) − n(A) = 30 − 6 = 24. Hence option A 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.
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