If U = {1, 2, …, 12}, A = {1, 2, 3, 4, 5, 6}, and B = {4, 5, 6, 7, 8}, what is (A − B)′?
Answer and explanation
Correct answer: {4, 5, 6, 7, 8, 9, 10, 11, 12}
The difference A − B contains the elements that are in A but not in B. Since A = {1, 2, 3, 4, 5, 6} and the common elements with B are {4, 5, 6}, we get A − B = {1, 2, 3}. The complement is taken with respect to U = {1, 2, …, 12}, so every element of U except 1, 2, and 3 remains. Thus (A − B)′ = {4, 5, 6, 7, 8, 9, 10, 11, 12}.
Frequently asked questions
What is the correct answer to this question?
{4, 5, 6, 7, 8, 9, 10, 11, 12}
Why is this the correct answer?
The difference A − B contains the elements that are in A but not in B. Since A = {1, 2, 3, 4, 5, 6} and the common elements with B are {4, 5, 6}, we get A − B = {1, 2, 3}. The complement is taken with respect to U = {1, 2, …, 12}, so every element of U except 1, 2, and 3 remains. Thus (A − B)′ = {4, 5, 6, 7, 8, 9, 10, 11, 12}.
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.
