If A = {1, 2} and B = P(A), what is n(B)?
Answer and explanation
Correct answer: 4
Set A contains two elements. For any finite set with n elements, its power set contains 2^n subsets because each element can either be included or excluded from a subset. Therefore, n(B) = n(P(A)) = 2^2 = 4. Explicitly, B = {∅, {1}, {2}, {1,2}}. The value 2 is n(A), not n(P(A)), while 8 would require a three-element original set.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Set A contains two elements. For any finite set with n elements, its power set contains 2^n subsets because each element can either be included or excluded from a subset. Therefore, n(B) = n(P(A)) = 2^2 = 4. Explicitly, B = {∅, {1}, {2}, {1,2}}. The value 2 is n(A), not n(P(A)), while 8 would require a three-element original set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
