If A = {k,l,m}, what is n(P(A))?
Answer and explanation
Correct answer: 8
A set containing n distinct elements has exactly 2ⁿ subsets, because each element can either be included in or excluded from a subset. Here A = {k,l,m} has three distinct elements. Therefore n(P(A)) = 2³ = 8. The power set includes the empty set, the three singleton subsets, the three two-element subsets, and A itself. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A set containing n distinct elements has exactly 2ⁿ subsets, because each element can either be included in or excluded from a subset. Here A = {k,l,m} has three distinct elements. Therefore n(P(A)) = 2³ = 8. The power set includes the empty set, the three singleton subsets, the three two-element subsets, and A itself. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
