If A has 4 elements and B has 5 elements with A⊂B, how many elements are in P(B)\P(A)?
Answer and explanation
Correct answer: 16
Since B has five elements, its power set contains |P(B)|=2^5=32 subsets. Since A has four elements, |P(A)|=2^4=16. Because A⊂B, every subset of A is also a subset of B, so P(A) is contained in P(B). Therefore, removing P(A) from P(B) leaves 32−16=16 elements. The strict inclusion ensures that the difference is meaningful, and option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Since B has five elements, its power set contains |P(B)|=2^5=32 subsets. Since A has four elements, |P(A)|=2^4=16. Because A⊂B, every subset of A is also a subset of B, so P(A) is contained in P(B). Therefore, removing P(A) from P(B) leaves 32−16=16 elements. The strict inclusion ensures that the difference is meaningful, and 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.
