If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), what is \(n(\mathcal{P}(A\setminus B))\)?
Answer and explanation
Correct answer: 8
Remove from A every element that belongs to B. Since B contains 2, 4, and 6, the difference is \(A\setminus B=\{1,3,5\}\), which has 3 elements. A set with n elements has exactly \(2^n\) subsets in its power set, because each element may either be selected or not selected. Therefore, \(n(\mathcal{P}(A\\setminus B))=2^3=8\). The number 3 is the size of the difference set, not of its power set.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Remove from A every element that belongs to B. Since B contains 2, 4, and 6, the difference is \(A\setminus B=\{1,3,5\}\), which has 3 elements. A set with n elements has exactly \(2^n\) subsets in its power set, because each element may either be selected or not selected. Therefore, \(n(\mathcal{P}(A\\setminus B))=2^3=8\). The number 3 is the size of the difference set, not of 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).
