If A = {1, 2, 3, 4, 5}, how many elements of P(A) contain both 2 and 5 but do not contain 1?
Answer and explanation
Correct answer: 4
We are counting subsets of A. The elements 2 and 5 are compulsory, while 1 is forbidden. The remaining elements 3 and 4 are unrestricted: each may either be included or excluded independently. Thus there are 2 choices for 3 and 2 choices for 4, giving 2 × 2 = 2^2 = 4 valid subsets. They are {2,5}, {2,3,5}, {2,4,5}, and {2,3,4,5}. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
We are counting subsets of A. The elements 2 and 5 are compulsory, while 1 is forbidden. The remaining elements 3 and 4 are unrestricted: each may either be included or excluded independently. Thus there are 2 choices for 3 and 2 choices for 4, giving 2 × 2 = 2^2 = 4 valid subsets. They are {2,5}, {2,3,5}, {2,4,5}, and {2,3,4,5}. 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.
