If U = {1,2,3,4,5,6,7,8}, A = {1,3,5,7}, and B = {2,3,5,8}, what is A' ∩ B'?
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Answer and explanation
Correct answer: {4,6}
Complements are taken relative to U. Thus A' = U − A = {2,4,6,8}, and B' = U − B = {1,4,6,7}. Their intersection contains the elements appearing in both lists, namely 4 and 6. Therefore A' ∩ B' = {4,6}, so option A is correct. Option B is A ∩ B, while the larger options confuse union with intersection.
Frequently asked questions
What is the correct answer to this question?
{4,6}
Why is this the correct answer?
Complements are taken relative to U. Thus A' = U − A = {2,4,6,8}, and B' = U − B = {1,4,6,7}. Their intersection contains the elements appearing in both lists, namely 4 and 6. Therefore A' ∩ B' = {4,6}, so option A is correct. Option B is A ∩ B, while the larger options confuse union with intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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