If \(A=\{1,2,3\}\) and \(B=\{3,4\}\), how many elements does \(\mathcal{P}(A\cap B)\) contain?
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Answer and explanation
Correct answer: 2
The only common element of A and B is 3, so \(A\cap B=\{3\}\). This intersection has one element. The power set of an n-element set contains \(2^n\) subsets, including the empty set and the original set. Therefore \(|\mathcal{P}(A\cap B)|=2^1=2\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The only common element of A and B is 3, so \(A\cap B=\{3\}\). This intersection has one element. The power set of an n-element set contains \(2^n\) subsets, including the empty set and the original set. Therefore \(|\mathcal{P}(A\cap B)|=2^1=2\), making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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