If U = {a, b, c, d, e, f, g, h}, A = {a, d, g}, and B = {b, d, e, h}, what is A′ ∩ B′?
Answer and explanation
Correct answer: {c, f}
A′ consists of the elements of U not in A: {b, c, e, f, h}. B′ consists of the elements of U not in B: {a, c, f, g}. Their intersection contains the elements common to both complements, namely c and f. Equivalently, by De Morgan’s law, A′ ∩ B′ = (A ∪ B)′; since A ∪ B = {a, b, d, e, g, h}, its complement in U is {c, f}.
Frequently asked questions
What is the correct answer to this question?
{c, f}
Why is this the correct answer?
A′ consists of the elements of U not in A: {b, c, e, f, h}. B′ consists of the elements of U not in B: {a, c, f, g}. Their intersection contains the elements common to both complements, namely c and f. Equivalently, by De Morgan’s law, A′ ∩ B′ = (A ∪ B)′; since A ∪ B = {a, b, d, e, g, h}, its complement in U is {c, f}.
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.
