If A = {1, 2, 3, 4, 5}, how many subsets contain 1 and exclude 5?
Answer and explanation
Correct answer: 8
The conditions fix the status of 1 and 5: 1 must be included and 5 must be excluded. The remaining elements 2, 3, and 4 are unrestricted, and each has two independent choices—either it is included or it is not. Hence the number of valid subsets is 2 × 2 × 2 = 2^3 = 8. No additional factor is needed because the required and forbidden elements are already fixed.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The conditions fix the status of 1 and 5: 1 must be included and 5 must be excluded. The remaining elements 2, 3, and 4 are unrestricted, and each has two independent choices—either it is included or it is not. Hence the number of valid subsets is 2 × 2 × 2 = 2^3 = 8. No additional factor is needed because the required and forbidden elements are already fixed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
