If A = {a, b, c, d}, how many proper subsets does A have?
Answer and explanation
Correct answer: 15
Set A has four elements, so its total number of subsets is 2⁴ = 16. A proper subset is any subset that is not equal to the original set A. The original set itself is one of the 16 subsets, so it must be excluded when counting proper subsets. Thus the number of proper subsets is 16 − 1 = 15. The empty set is included among these proper subsets.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
Set A has four elements, so its total number of subsets is 2⁴ = 16. A proper subset is any subset that is not equal to the original set A. The original set itself is one of the 16 subsets, so it must be excluded when counting proper subsets. Thus the number of proper subsets is 16 − 1 = 15. The empty set is included among these proper subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
