How many proper subsets does a set with four elements have?
Answer and explanation
Correct answer: 15
A set with n elements has 2^n total subsets. For four elements, this gives 2^4 = 16 subsets. A proper subset is any subset that is not equal to the original set, so the original set itself must be excluded from the total. Therefore the number of proper subsets is 16 − 1 = 15. The empty set is included because it is a proper subset of every non-empty set. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A set with n elements has 2^n total subsets. For four elements, this gives 2^4 = 16 subsets. A proper subset is any subset that is not equal to the original set, so the original set itself must be excluded from the total. Therefore the number of proper subsets is 16 − 1 = 15. The empty set is included because it is a proper subset of every non-empty set. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
