If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5, 6}, and B = {4, 5, 6, 7, 8}, what is (A \ B)ᶜ?
Answer and explanation
Correct answer: {4, 5, 6, 7, 8, 9, 10}
First find the difference A \ B. The common elements 4, 5, and 6 are removed from A, leaving A \ B = {1, 2, 3}. The complement is taken relative to U, so it contains every element of U except 1, 2, and 3. Hence (A \ B)ᶜ = {4, 5, 6, 7, 8, 9, 10}, which is option B. Option A is the difference itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{4, 5, 6, 7, 8, 9, 10}
Why is this the correct answer?
First find the difference A \ B. The common elements 4, 5, and 6 are removed from A, leaving A \ B = {1, 2, 3}. The complement is taken relative to U, so it contains every element of U except 1, 2, and 3. Hence (A \ B)ᶜ = {4, 5, 6, 7, 8, 9, 10}, which is option B. Option A is the difference itself, not its complement.
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.
