If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6, 8}, how many members of P(U) are disjoint from A'?
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Answer and explanation
Correct answer: 16
With respect to U, A' = {1, 3, 5, 7}. A subset S of U is disjoint from A' exactly when S contains none of 1, 3, 5, or 7. Therefore S can contain only elements of A = {2, 4, 6, 8}. Every subset of A is disjoint from A', and A has 4 elements, so the number is 2^4 = 16. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
With respect to U, A' = {1, 3, 5, 7}. A subset S of U is disjoint from A' exactly when S contains none of 1, 3, 5, or 7. Therefore S can contain only elements of A = {2, 4, 6, 8}. Every subset of A is disjoint from A', and A has 4 elements, so the number is 2^4 = 16. 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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