If A = {1, 2, 3, 4, 5}, how many subsets must contain 1?
Answer and explanation
Correct answer: 16
The element 1 is required, so it is fixed as included in every counted subset. The remaining four elements—2, 3, 4, and 5—can each be independently included or excluded. That gives 2 choices for each of four elements, so the number of subsets is 2⁴ = 16. Equivalently, exactly half of the 2⁵ = 32 total subsets contain any specified element. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The element 1 is required, so it is fixed as included in every counted subset. The remaining four elements—2, 3, 4, and 5—can each be independently included or excluded. That gives 2 choices for each of four elements, so the number of subsets is 2⁴ = 16. Equivalently, exactly half of the 2⁵ = 32 total subsets contain any specified element. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
