If U = {a, b, c, d, e}, A = {a, c, e}, and B = {b, e}, what is (A ∪ B)'?
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Answer and explanation
Correct answer: {d}
First form the union: A ∪ B = {a, c, e} ∪ {b, e} = {a, b, c, e}. The complement contains the elements of U that are absent from this union. Since d is the only element of U not in A ∪ B, (A ∪ B)' = {d}. Therefore option A is correct. The complement must be taken relative to U.
Frequently asked questions
What is the correct answer to this question?
{d}
Why is this the correct answer?
First form the union: A ∪ B = {a, c, e} ∪ {b, e} = {a, b, c, e}. The complement contains the elements of U that are absent from this union. Since d is the only element of U not in A ∪ B, (A ∪ B)' = {d}. Therefore option A is correct. The complement must be taken relative to U.
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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