If U = {1,2,3,...,80} and A is the subset of U whose elements are divisible by 8, how many elements does Aᶜ contain?
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Answer and explanation
Correct answer: 70
The positive multiples of 8 from 1 through 80 are 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, so A has 10 elements. The complement contains all remaining elements of U. Therefore n(Aᶜ) = n(U) − n(A) = 80 − 10 = 70. Option B counts A itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
70
Why is this the correct answer?
The positive multiples of 8 from 1 through 80 are 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, so A has 10 elements. The complement contains all remaining elements of U. Therefore n(Aᶜ) = n(U) − n(A) = 80 − 10 = 70. Option B counts A itself, not its complement.
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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