If A = {a, b, c}, how many proper subsets does A have?
Answer and explanation
Correct answer: 7
A set with three elements has 2³ = 8 total subsets. A proper subset is a subset that is not equal to the original set itself. The only subset that must be excluded from the total is A = {a,b,c}; the empty set and all other smaller subsets are proper subsets. Therefore the number of proper subsets is 8 − 1 = 7, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A set with three elements has 2³ = 8 total subsets. A proper subset is a subset that is not equal to the original set itself. The only subset that must be excluded from the total is A = {a,b,c}; the empty set and all other smaller subsets are proper subsets. Therefore the number of proper subsets is 8 − 1 = 7, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
