If \(A=\{2,5,7\}\), what is \(n(\mathcal{P}(A))\)?
Answer and explanation
Correct answer: 8
The set \(A=\{2,5,7\}\) contains 3 distinct elements, so \(n(A)=3\). For a finite set with \(n\) elements, every element has two choices in forming a subset: it is either included or excluded. Consequently, the number of subsets, and hence the number of elements in the power set, is \(2^n\). Therefore, \(n(\mathcal{P}(A))=2^3=8\).
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The set \(A=\{2,5,7\}\) contains 3 distinct elements, so \(n(A)=3\). For a finite set with \(n\) elements, every element has two choices in forming a subset: it is either included or excluded. Consequently, the number of subsets, and hence the number of elements in the power set, is \(2^n\). Therefore, \(n(\mathcal{P}(A))=2^3=8\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
