If A = {2, 3, 5, 7}, how many subsets of A contain both elements 2 and 7?
Answer and explanation
Correct answer: 4
The elements 2 and 7 are required in every counted subset, so they are fixed and do not create choices. The remaining elements, 3 and 5, may independently be included or omitted. Thus there are 2 choices for 3 and 2 choices for 5, giving 2 × 2 = 4 subsets. They are {2,7}, {2,3,7}, {2,5,7}, and {2,3,5,7}. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The elements 2 and 7 are required in every counted subset, so they are fixed and do not create choices. The remaining elements, 3 and 5, may independently be included or omitted. Thus there are 2 choices for 3 and 2 choices for 5, giving 2 × 2 = 4 subsets. They are {2,7}, {2,3,7}, {2,5,7}, and {2,3,5,7}. 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.
