Given U = {1, 2, 3, ..., 12}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6, 7}, what is (Aᶜ ∩ B)ᶜ?
Answer and explanation
Correct answer: {1, 2, 3, 4, 8, 9, 10, 11, 12}
All complements are taken with respect to U. First, Aᶜ = U − A = {5, 6, 7, 8, 9, 10, 11, 12}. Intersecting this with B = {3, 4, 5, 6, 7} gives Aᶜ ∩ B = {5, 6, 7}. Now take the complement of this result in U: (Aᶜ ∩ B)ᶜ = U − {5, 6, 7} = {1, 2, 3, 4, 8, 9, 10, 11, 12}. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4, 8, 9, 10, 11, 12}
Why is this the correct answer?
All complements are taken with respect to U. First, Aᶜ = U − A = {5, 6, 7, 8, 9, 10, 11, 12}. Intersecting this with B = {3, 4, 5, 6, 7} gives Aᶜ ∩ B = {5, 6, 7}. Now take the complement of this result in U: (Aᶜ ∩ B)ᶜ = U − {5, 6, 7} = {1, 2, 3, 4, 8, 9, 10, 11, 12}. Thus, 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.
