If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2\}\), how many elements are in \(\mathcal{P}(A')\)?
Advertisement
Answer and explanation
Correct answer: 16
First find the complement of \(A\) in the universal set: \(A'=U-A=\{3,4,5,6\}\). Thus, \(A'\) has 4 elements. For any finite set with \(n\) elements, the power set has \(2^n\) elements, because each element can independently be selected or not selected. Therefore, \(|\mathcal{P}(A')|=2^4=16\).
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
First find the complement of \(A\) in the universal set: \(A'=U-A=\{3,4,5,6\}\). Thus, \(A'\) has 4 elements. For any finite set with \(n\) elements, the power set has \(2^n\) elements, because each element can independently be selected or not selected. Therefore, \(|\mathcal{P}(A')|=2^4=16\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement