If U = {a, b, c, d, e}, A = {a, c}, and B = {c, d}, what is the number of elements of P((A ∪ B)')?
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Answer and explanation
Correct answer: 4
First find the union: A ∪ B = {a, c, d}. The complement is taken relative to U, so (A ∪ B)' = U − {a, c, d} = {b, e}. This set has two elements. A set with n elements has 2ⁿ subsets in its power set; therefore, n(P((A ∪ B)')) = 2² = 4. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
First find the union: A ∪ B = {a, c, d}. The complement is taken relative to U, so (A ∪ B)' = U − {a, c, d} = {b, e}. This set has two elements. A set with n elements has 2ⁿ subsets in its power set; therefore, n(P((A ∪ B)')) = 2² = 4. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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