If n(𝒫(B)) = 128, how many proper subsets does B have?
Answer and explanation
Correct answer: 127
The value n(𝒫(B)) = 128 tells us that B has 128 subsets in total. Every set is a subset of itself, but it is not a proper subset of itself. Therefore, exactly one subset—the set B—is removed when counting proper subsets. The number of proper subsets is 128 − 1 = 127. Although 128 = 2⁷ also shows that B has seven elements, that value is not the requested answer.
Frequently asked questions
What is the correct answer to this question?
127
Why is this the correct answer?
The value n(𝒫(B)) = 128 tells us that B has 128 subsets in total. Every set is a subset of itself, but it is not a proper subset of itself. Therefore, exactly one subset—the set B—is removed when counting proper subsets. The number of proper subsets is 128 − 1 = 127. Although 128 = 2⁷ also shows that B has seven elements, that value is not the requested answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
