If \(A=\{a,b,c\}\), how many elements of \(\mathcal{P}(A)\) are supersets of \(\{a,b\}\)?
Answer and explanation
Correct answer: 2
A superset of \(\{a,b\}\) must contain both \(a\) and \(b\). The only remaining element of \(A\) is \(c\), and it may either be excluded or included. Thus the two possible supersets are \(\{a,b\}\) and \(\{a,b,c\}\). In general, if \(S\subseteq A\), the number of supersets of \(S\) contained in \(A\) is \(2^{|A|-|S|}\); here this is \(2^{3-2}=2\).
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
A superset of \(\{a,b\}\) must contain both \(a\) and \(b\). The only remaining element of \(A\) is \(c\), and it may either be excluded or included. Thus the two possible supersets are \(\{a,b\}\) and \(\{a,b,c\}\). In general, if \(S\subseteq A\), the number of supersets of \(S\) contained in \(A\) is \(2^{|A|-|S|}\); here this is \(2^{3-2}=2\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
