If A={1,2,3,4,5}, how many elements of the power set P(A) contain at least one of 2 and 3?
Answer and explanation
Correct answer: 24
A has five elements, so its power set contains 2^5=32 subsets. To count subsets containing at least one of 2 or 3, use the complement method. A subset contains neither 2 nor 3 only when it is formed from the remaining three elements {1,4,5}; this gives 2^3=8 subsets. Thus the required number is 32−8=24. Equivalently, count subsets containing 2 or 3 and subtract those containing both if using inclusion-exclusion. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
A has five elements, so its power set contains 2^5=32 subsets. To count subsets containing at least one of 2 or 3, use the complement method. A subset contains neither 2 nor 3 only when it is formed from the remaining three elements {1,4,5}; this gives 2^3=8 subsets. Thus the required number is 32−8=24. Equivalently, count subsets containing 2 or 3 and subtract those containing both if using inclusion-exclusion. 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.
