If U = {1, 2, ..., 45} and A = {x : x ∈ U, 9 divides x}, how many elements divisible by 3 are in A'?
Answer and explanation
Correct answer: 10
The multiples of 3 in U are 3, 6, ..., 45, so there are 45 ÷ 3 = 15 such elements. The set A contains the multiples of 9: 9, 18, 27, 36, and 45, giving 45 ÷ 9 = 5 elements. Every multiple of 9 is also a multiple of 3, so the multiples of 3 that lie in A' are 15 − 5 = 10. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The multiples of 3 in U are 3, 6, ..., 45, so there are 45 ÷ 3 = 15 such elements. The set A contains the multiples of 9: 9, 18, 27, 36, and 45, giving 45 ÷ 9 = 5 elements. Every multiple of 9 is also a multiple of 3, so the multiples of 3 that lie in A' are 15 − 5 = 10. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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