If A = {1, 2, 3, 4, 5}, how many subsets contain 2 and do not contain 4?
Answer and explanation
Correct answer: 8
The element 2 is required, so it is fixed as included in every acceptable subset. The element 4 is forbidden, so it is fixed as excluded. The remaining elements 1, 3, and 5 are unrestricted; each may be selected or not selected independently. Thus there are 2 choices for each of three free elements, giving 2³ = 8 valid subsets. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 2 is required, so it is fixed as included in every acceptable subset. The element 4 is forbidden, so it is fixed as excluded. The remaining elements 1, 3, and 5 are unrestricted; each may be selected or not selected independently. Thus there are 2 choices for each of three free elements, giving 2³ = 8 valid subsets. 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.
