Let U = {x ∈ N : x ≤ 10}, and let A be the set of prime numbers in U. What is A′?
Answer and explanation
Correct answer: {1, 4, 6, 8, 9, 10}
Assuming N = {1,2,3,...}, the universal set is U = {1,2,3,4,5,6,7,8,9,10}. The primes in U are A = {2,3,5,7}. The complement A′ contains every member of U that is not prime, giving {1,4,6,8,9,10}. Number 1 is neither prime nor composite, so it correctly belongs to the complement. Option B is A itself, not A′.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 6, 8, 9, 10}
Why is this the correct answer?
Assuming N = {1,2,3,...}, the universal set is U = {1,2,3,4,5,6,7,8,9,10}. The primes in U are A = {2,3,5,7}. The complement A′ contains every member of U that is not prime, giving {1,4,6,8,9,10}. Number 1 is neither prime nor composite, so it correctly belongs to the complement. Option B is A itself, not A′.
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.
