If \(A=\{1,2,3,4,5\}\), how many subsets contain 1 and do not contain 2?
Answer and explanation
Correct answer: 8
The condition requires 1 to be included and 2 to be excluded, so both of these elements have fixed choices. The remaining elements 3, 4, and 5 are unrestricted; each can either be included or left out independently. Therefore, the number of possible subsets is \(2\times2\times2=2^3=8\). For example, \{1\}, \{1,3\}, and \{1,4,5\} are valid, while any subset containing 2 is invalid. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The condition requires 1 to be included and 2 to be excluded, so both of these elements have fixed choices. The remaining elements 3, 4, and 5 are unrestricted; each can either be included or left out independently. Therefore, the number of possible subsets is \(2\times2\times2=2^3=8\). For example, \{1\}, \{1,3\}, and \{1,4,5\} are valid, while any subset containing 2 is invalid. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
