Let U = {1, 2, ..., 21} and A = {x : x is divisible by 3}. How many odd elements are there in A′, the complement of A in U?
Answer and explanation
Correct answer: 7
The universal set U contains the integers from 1 through 21. Its odd elements are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21, so there are 11 odd numbers. Among these, 3, 9, 15, and 21 are divisible by 3 and therefore belong to A, not A′. Removing them leaves 11 − 4 = 7 odd elements in A′. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The universal set U contains the integers from 1 through 21. Its odd elements are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21, so there are 11 odd numbers. Among these, 3, 9, 15, and 21 are divisible by 3 and therefore belong to A, not A′. Removing them leaves 11 − 4 = 7 odd elements in A′. Hence, option B 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.
