If A = {1,2,3,4}, how many elements of P(A) contain 1 or have size 2?
Answer and explanation
Correct answer: 11
There are 2³ = 8 subsets of A that contain 1, because the other three elements may be chosen freely. There are C(4,2) = 6 two-element subsets. Some subsets belong to both groups: a two-element subset containing 1 is formed by choosing one of the remaining three elements, giving C(3,1) = 3. By inclusion–exclusion, the required count is 8 + 6 − 3 = 11. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
There are 2³ = 8 subsets of A that contain 1, because the other three elements may be chosen freely. There are C(4,2) = 6 two-element subsets. Some subsets belong to both groups: a two-element subset containing 1 is formed by choosing one of the remaining three elements, giving C(3,1) = 3. By inclusion–exclusion, the required count is 8 + 6 − 3 = 11. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
