If A = {1, 2, 3, 4}, how many subsets of A have at least one element?
Answer and explanation
Correct answer: 15
A set with n elements has 2ⁿ total subsets because every element can either be selected or not selected. Here n = 4, so A has 2⁴ = 16 subsets. Exactly one of these is the empty set, which has no elements. Therefore, the number of subsets containing at least one element is 16 − 1 = 15. Hence option B is correct; option C includes the empty set and is therefore too large.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A set with n elements has 2ⁿ total subsets because every element can either be selected or not selected. Here n = 4, so A has 2⁴ = 16 subsets. Exactly one of these is the empty set, which has no elements. Therefore, the number of subsets containing at least one element is 16 − 1 = 15. Hence option B is correct; option C includes the empty set and is therefore too large.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
