If \(U=\{a,b,c,d,e\}\) and \(A=\{a,c,e\}\), how many members does \(\mathcal{P}(A')\) have?
Advertisement
Answer and explanation
Correct answer: 4
The complement is taken with respect to the given universal set. Removing the elements of \(A\) from \(U\) gives \(A'=U-A=\{b,d\}\), so \(n(A')=2\). The power set of a set containing two elements has \(2^2=4\) members: \(\varnothing\), \(\{b\}\), \(\{d\}\), and \(\{b,d\}\). Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The complement is taken with respect to the given universal set. Removing the elements of \(A\) from \(U\) gives \(A'=U-A=\{b,d\}\), so \(n(A')=2\). The power set of a set containing two elements has \(2^2=4\) members: \(\varnothing\), \(\{b\}\), \(\{d\}\), and \(\{b,d\}\). Hence 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.
Advertisement