If n(A) = 2, what is n(P(A))?
Answer and explanation
Correct answer: 4
For a finite set A with n(A) elements, the number of elements in its power set is n(P(A)) = 2ⁿ. Each element of A has two choices when forming a subset: it is either included or excluded. With n(A) = 2, there are 2² = 4 possible subsets. They are ∅, the two singleton subsets, and A itself. Therefore, option C, 4, is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a finite set A with n(A) elements, the number of elements in its power set is n(P(A)) = 2ⁿ. Each element of A has two choices when forming a subset: it is either included or excluded. With n(A) = 2, there are 2² = 4 possible subsets. They are ∅, the two singleton subsets, and A itself. Therefore, option C, 4, is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
