If \(A\) has 2 elements and \(B\) has 3 elements with \(A\subset B\), how many elements are in \(\mathcal{P}(B)\setminus\mathcal{P}(A)\)?
Answer and explanation
Correct answer: 4
For a finite set with \(n\) elements, the power set contains \(2^n\) subsets. Therefore, \(|\mathcal{P}(B)|=2^3=8\) and \(|\mathcal{P}(A)|=2^2=4\). Because \(A\subset B\), every subset of \(A\) is a subset of \(B\), so \(\mathcal{P}(A)\subseteq\mathcal{P}(B)\). The difference therefore has \(8-4=4\) elements. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a finite set with \(n\) elements, the power set contains \(2^n\) subsets. Therefore, \(|\mathcal{P}(B)|=2^3=8\) and \(|\mathcal{P}(A)|=2^2=4\). Because \(A\subset B\), every subset of \(A\) is a subset of \(B\), so \(\mathcal{P}(A)\subseteq\mathcal{P}(B)\). The difference therefore has \(8-4=4\) elements. Thus 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.
