If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, and B = {4, 5, 6}, what is A' ∩ B, where the complement is taken with respect to U?
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Answer and explanation
Correct answer: {5, 6}
The complement of A relative to U is A' = {5, 6, 7, 8, 9}, because these are the elements of U not belonging to A. Now intersect A' with B = {4, 5, 6}. The common elements are 5 and 6; 4 is excluded because it belongs to A. Hence, A' ∩ B = {5, 6}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{5, 6}
Why is this the correct answer?
The complement of A relative to U is A' = {5, 6, 7, 8, 9}, because these are the elements of U not belonging to A. Now intersect A' with B = {4, 5, 6}. The common elements are 5 and 6; 4 is excluded because it belongs to A. Hence, A' ∩ B = {5, 6}, 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.
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