If A = {1, 2, 3, 4}, how many subsets of A contain 1 and do not contain 4?
Answer and explanation
Correct answer: 4
The element 1 is compulsory, so it has no choice: it must be included. The element 4 is forbidden, so it also has no choice: it must be excluded. Only 2 and 3 are free, and each can independently be included or excluded. Therefore the number of valid subsets is 2 × 2 = 2² = 4. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The element 1 is compulsory, so it has no choice: it must be included. The element 4 is forbidden, so it also has no choice: it must be excluded. Only 2 and 3 are free, and each can independently be included or excluded. Therefore the number of valid subsets is 2 × 2 = 2² = 4. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
