If A = {2, 3, 5, 7}, how many subsets contain 2 but do not contain 7?
Answer and explanation
Correct answer: 4
The element 2 is required, so it has no choice: it must be included. The element 7 is prohibited, so it also has no choice: it must be excluded. Only 3 and 5 remain free, and each can independently be included or excluded. Consequently, the number of valid subsets is 2² = 4. They are {2}, {2,3}, {2,5}, and {2,3,5}; therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The element 2 is required, so it has no choice: it must be included. The element 7 is prohibited, so it also has no choice: it must be excluded. Only 3 and 5 remain free, and each can independently be included or excluded. Consequently, the number of valid subsets is 2² = 4. They are {2}, {2,3}, {2,5}, and {2,3,5}; therefore 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.
