How many proper subsets does a set with three elements have?
Advertisement
Answer and explanation
Correct answer: 7
A set with n elements has 2ⁿ subsets because each element can either be included or excluded. For three elements, the total number of subsets is 2³ = 8. A proper subset is any subset other than the set itself, so we exclude exactly one subset, namely the original set. Therefore, the number of proper subsets is 8 − 1 = 7.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A set with n elements has 2ⁿ subsets because each element can either be included or excluded. For three elements, the total number of subsets is 2³ = 8. A proper subset is any subset other than the set itself, so we exclude exactly one subset, namely the original set. Therefore, the number of proper subsets is 8 − 1 = 7.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement