If A is a subset of B, n(A) = 3, and n(B) = 5, how many elements does the set P(B) − P(A) contain? Here, P(X) denotes the power set of X.
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Answer and explanation
Correct answer: 24
A set with n elements has 2^n subsets, so its power set contains 2^n elements. Therefore, n(P(B)) = 2^5 = 32 and n(P(A)) = 2^3 = 8. Since A is a subset of B, every subset of A is also a subset of B; hence P(A) is a subset of P(B). Thus, P(B) − P(A) contains 32 − 8 = 24 elements. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
A set with n elements has 2^n subsets, so its power set contains 2^n elements. Therefore, n(P(B)) = 2^5 = 32 and n(P(A)) = 2^3 = 8. Since A is a subset of B, every subset of A is also a subset of B; hence P(A) is a subset of P(B). Thus, P(B) − P(A) contains 32 − 8 = 24 elements. Therefore, 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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