If \(A=\{\emptyset,5,10\}\), what is \(n(\mathcal{P}(A))\)?
Answer and explanation
Correct answer: 8
The symbol \(\emptyset\) is one element of \(A\); it is not the same as saying that the set has no elements. Thus the three distinct elements of \(A\) are \(\emptyset\), 5, and 10, so \(n(A)=3\). For a finite set with \(n\) elements, the power set has \(2^n\) elements because each element can be selected or not selected. Therefore, \(n(\mathcal{P}(A))=2^3=8\), making option C correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The symbol \(\emptyset\) is one element of \(A\); it is not the same as saying that the set has no elements. Thus the three distinct elements of \(A\) are \(\emptyset\), 5, and 10, so \(n(A)=3\). For a finite set with \(n\) elements, the power set has \(2^n\) elements because each element can be selected or not selected. Therefore, \(n(\mathcal{P}(A))=2^3=8\), making option C correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
