If U = {1, 2, ..., 27} and A = {x : x ∈ U, 3 divides x}, how many elements divisible by 2 are in A′?
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Answer and explanation
Correct answer: 9
The even numbers in U from 1 to 27 are 2, 4, 6, ..., 26, so there are 13 of them. Among these, the numbers 6, 12, 18, and 24 are divisible by 3 and therefore belong to A, not A′. Hence the even elements in A′ are 13 − 4 = 9. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The even numbers in U from 1 to 27 are 2, 4, 6, ..., 26, so there are 13 of them. Among these, the numbers 6, 12, 18, and 24 are divisible by 3 and therefore belong to A, not A′. Hence the even elements in A′ are 13 − 4 = 9. Thus, 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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