What is the number of proper subsets of a 4-element set?
Answer and explanation
Correct answer: 15
An n-element set has 2ⁿ total subsets because every element can independently be included or excluded. For n = 4, the total is 2⁴ = 16. A proper subset is a subset that is not equal to the original set, so the original set must be removed from this count. Therefore, the number of proper subsets is 16 − 1 = 15. Option B counts the original set too, while 8 and 14 do not follow from the proper-subset formula.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
An n-element set has 2ⁿ total subsets because every element can independently be included or excluded. For n = 4, the total is 2⁴ = 16. A proper subset is a subset that is not equal to the original set, so the original set must be removed from this count. Therefore, the number of proper subsets is 16 − 1 = 15. Option B counts the original set too, while 8 and 14 do not follow from the proper-subset formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
