If U = {1, 2, ..., 64} and A = {x : x ∈ U, x = 2^k where k ∈ N₀}, how many numbers divisible by 4 are in A′?
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Answer and explanation
Correct answer: 11
The multiples of 4 in U = {1, ..., 64} are 4, 8, 12, ..., 64, so their number is 64/4 = 16. Among them, the members of A are powers of 2: 4 = 2², 8 = 2³, 16 = 2⁴, 32 = 2⁵, and 64 = 2⁶, giving five numbers. These five are excluded from A′. Hence the required count is 16 − 5 = 11, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The multiples of 4 in U = {1, ..., 64} are 4, 8, 12, ..., 64, so their number is 64/4 = 16. Among them, the members of A are powers of 2: 4 = 2², 8 = 2³, 16 = 2⁴, 32 = 2⁵, and 64 = 2⁶, giving five numbers. These five are excluded from A′. Hence the required count is 16 − 5 = 11, so 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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