If U = {1, 2, 3, 4} and A = ∅, how many elements are in P(A')?
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Answer and explanation
Correct answer: 16
Since A is the empty set, its complement relative to U is A' = U = {1, 2, 3, 4}. This set has four elements. The power set of a finite set with four elements contains 2^4 subsets, because each element can independently be included or excluded. Thus n(P(A')) = 16.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Since A is the empty set, its complement relative to U is A' = U = {1, 2, 3, 4}. This set has four elements. The power set of a finite set with four elements contains 2^4 subsets, because each element can independently be included or excluded. Thus n(P(A')) = 16.
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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