If U = {a, b, c, d, e, f, g, h}, A' = {b, d, f, h}, and B = {a, b, c, d}, what is A ∩ B'?
Answer and explanation
Correct answer: {e, g}
The governing idea is that a complement is taken relative to the universal set U. Since A' = {b, d, f, h}, the elements of A are the remaining members: A = {a, c, e, g}. Also, B' = U − B = {e, f, g, h}. The intersection contains elements common to both sets, namely e and g. Thus A ∩ B' = {e, g}; option A is correct. Options B, C and D contain elements excluded from one of the required sets.
Frequently asked questions
What is the correct answer to this question?
{e, g}
Why is this the correct answer?
The governing idea is that a complement is taken relative to the universal set U. Since A' = {b, d, f, h}, the elements of A are the remaining members: A = {a, c, e, g}. Also, B' = U − B = {e, f, g, h}. The intersection contains elements common to both sets, namely e and g. Thus A ∩ B' = {e, g}; option A is correct. Options B, C and D contain elements excluded from one of the required sets.
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.
