If U = {1,2,3,4,5,6,7,8,9}, A = {2,3,5,7}, and B = {1,2,3,4,5}, what is the complement of B − A with respect to U?
Answer and explanation
Correct answer: {2,3,5,6,7,8,9}
The difference B − A contains elements that belong to B but not to A. From B = {1,2,3,4,5}, removing 2, 3, and 5 gives B − A = {1,4}. Its complement relative to U contains every element of U except 1 and 4. Consequently, (B − A)ᶜ = {2,3,5,6,7,8,9}. Option B is the difference itself, not its complement, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{2,3,5,6,7,8,9}
Why is this the correct answer?
The difference B − A contains elements that belong to B but not to A. From B = {1,2,3,4,5}, removing 2, 3, and 5 gives B − A = {1,4}. Its complement relative to U contains every element of U except 1 and 4. Consequently, (B − A)ᶜ = {2,3,5,6,7,8,9}. Option B is the difference itself, not its complement, so 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.
