If \(A=\{1,2,3,4\}\), how many elements of \(\mathcal{P}(A)\) contain exactly one of \(1\) and \(2\)?
Answer and explanation
Correct answer: 8
A subset must contain exactly one of the elements \(1\) and \(2\). There are two choices for this part: include \(1\) but not \(2\), or include \(2\) but not \(1\). The remaining elements \(3\) and \(4\) can independently be included or excluded, giving \(2^2=4\) choices. Therefore the total is \(2\times4=8\), so option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset must contain exactly one of the elements \(1\) and \(2\). There are two choices for this part: include \(1\) but not \(2\), or include \(2\) but not \(1\). The remaining elements \(3\) and \(4\) can independently be included or excluded, giving \(2^2=4\) choices. Therefore the total is \(2\times4=8\), so 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.
