If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), how many elements are there in the power set \(\mathcal{P}(A-B)\)?
Answer and explanation
Correct answer: 4
The difference \(A-B\) contains elements that are in \(A\) but not in \(B\). Therefore, \(A-B=\{1,2\}\), which has 2 elements. If a finite set has \(n\) elements, its power set has exactly \(2^n\) subsets, including the empty set and the original set. Hence, \(|\mathcal{P}(A-B)|=2^2=4\). Option B gives only the cardinality of \(A-B\), not its power set.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The difference \(A-B\) contains elements that are in \(A\) but not in \(B\). Therefore, \(A-B=\{1,2\}\), which has 2 elements. If a finite set has \(n\) elements, its power set has exactly \(2^n\) subsets, including the empty set and the original set. Hence, \(|\mathcal{P}(A-B)|=2^2=4\). Option B gives only the cardinality of \(A-B\), not its power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
