If \(A=\{1,2,3,4\}\) and \(U=\{1,2,3,4,5,6\}\), how many members of \(\mathcal{P}(A)\) are subsets of \(U\)?
Answer and explanation
Correct answer: 16
Every member of \(\mathcal{P}(A)\) is, by definition, a subset of \(A\). Since every element of \(A\) is also in \(U\), we have \(A\subseteq U\). Consequently, every subset of \(A\) is automatically a subset of \(U\). A set with four elements has \(2^4=16\) subsets, including the empty set and the set \(A\) itself. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Every member of \(\mathcal{P}(A)\) is, by definition, a subset of \(A\). Since every element of \(A\) is also in \(U\), we have \(A\subseteq U\). Consequently, every subset of \(A\) is automatically a subset of \(U\). A set with four elements has \(2^4=16\) subsets, including the empty set and the set \(A\) itself. 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.
