If (A\subseteq B), (|A|=3), and (|B|=6), what is (|\mathcal{P}(B)-\mathcal{P}(A)|)?
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Answer and explanation
Correct answer: 56
Because A is a subset of B, every subset of A is also a subset of B; therefore P(A) is contained in P(B). The difference P(B)-P(A) contains all subsets of B except the 2^3 subsets of A. Since |P(B)|=2^6=64 and |P(A)|=2^3=8, the difference has 64-8=56 elements. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
56
Why is this the correct answer?
Because A is a subset of B, every subset of A is also a subset of B; therefore P(A) is contained in P(B). The difference P(B)-P(A) contains all subsets of B except the 2^3 subsets of A. Since |P(B)|=2^6=64 and |P(A)|=2^3=8, the difference has 64-8=56 elements. Option C 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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