If A = {1,2,3,4,5}, how many elements of P(A) do not contain 1 and must contain 2?
Answer and explanation
Correct answer: 8
The element 1 is forbidden, while 2 is compulsory. After fixing these conditions, the remaining elements 3, 4, and 5 may each be either included or excluded independently. Thus there are 2 choices for each of three unrestricted elements, giving 2³ = 8 valid subsets. The compulsory element 2 does not add a choice, and the forbidden element 1 has no choice. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 1 is forbidden, while 2 is compulsory. After fixing these conditions, the remaining elements 3, 4, and 5 may each be either included or excluded independently. Thus there are 2 choices for each of three unrestricted elements, giving 2³ = 8 valid subsets. The compulsory element 2 does not add a choice, and the forbidden element 1 has no choice. 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.
