If U = {1, 2, ..., 25} and A = {x ∈ U : 5 is a divisor of x}, how many prime numbers are in A′?
Answer and explanation
Correct answer: 8
The prime numbers from 1 through 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23, so there are 9 primes. Set A contains the multiples of 5, including 5 itself. Among the primes, only 5 belongs to A; every other listed prime belongs to A′. Therefore the number of primes in A′ is 9 − 1 = 8. Hence option C, not option A, is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The prime numbers from 1 through 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23, so there are 9 primes. Set A contains the multiples of 5, including 5 itself. Among the primes, only 5 belongs to A; every other listed prime belongs to A′. Therefore the number of primes in A′ is 9 − 1 = 8. Hence option C, not 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.
