If U = {1, 2, ..., 25} and A is the set of non-prime elements of U, what is A'?
Answer and explanation
Correct answer: {2, 3, 5, 7, 11, 13, 17, 19, 23}
A contains every number in U that is not prime. Therefore its complement contains exactly the prime numbers in U. The primes from 1 through 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23. Note that 1 is neither prime nor composite, so it remains in A rather than A'. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{2, 3, 5, 7, 11, 13, 17, 19, 23}
Why is this the correct answer?
A contains every number in U that is not prime. Therefore its complement contains exactly the prime numbers in U. The primes from 1 through 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23. Note that 1 is neither prime nor composite, so it remains in A rather than A'. Hence 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.
