If U = {1, 2, ..., 9}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, what is the complement of A ∩ B with respect to U?
Answer and explanation
Correct answer: {1, 2, 5, 6, 7, 8, 9}
The intersection A ∩ B contains the elements common to both sets. Since A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, we get A ∩ B = {3, 4}. The complement is taken within the universal set U, so remove 3 and 4 from U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Therefore, (A ∩ B)' = {1, 2, 5, 6, 7, 8, 9}.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 5, 6, 7, 8, 9}
Why is this the correct answer?
The intersection A ∩ B contains the elements common to both sets. Since A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, we get A ∩ B = {3, 4}. The complement is taken within the universal set U, so remove 3 and 4 from U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Therefore, (A ∩ B)' = {1, 2, 5, 6, 7, 8, 9}.
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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