If n(A) = 4, how many proper subsets does A have?
Answer and explanation
Correct answer: 15
A set with four elements has 2^4 = 16 total subsets. A proper subset is a subset that is not equal to the original set A itself. Since exactly one of the 16 subsets is A, subtract it from the total: 16 − 1 = 15. The empty set is included among the proper subsets. Therefore, A has 15 proper subsets, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A set with four elements has 2^4 = 16 total subsets. A proper subset is a subset that is not equal to the original set A itself. Since exactly one of the 16 subsets is A, subtract it from the total: 16 − 1 = 15. The empty set is included among the proper subsets. Therefore, A has 15 proper subsets, 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.
