If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6, 8}, what is n(P(A'))?
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Answer and explanation
Correct answer: 16
The complement is taken relative to U. Removing the elements of A from U gives A' = U \ A = {1, 3, 5, 7}, so A' has 4 elements. The power set of a four-element set has 2^4 subsets, because each element can either be included or excluded. Therefore n(P(A')) = 16, making option C correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The complement is taken relative to U. Removing the elements of A from U gives A' = U \ A = {1, 3, 5, 7}, so A' has 4 elements. The power set of a four-element set has 2^4 subsets, because each element can either be included or excluded. Therefore n(P(A')) = 16, making option C 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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