If A = {1,2,3,4,5}, how many elements of P(A) have at most 2 elements?
Answer and explanation
Correct answer: 16
“At most 2” means the subset may contain 0, 1, or 2 elements. The numbers of such subsets are C(5,0)=1, C(5,1)=5, and C(5,2)=10. Adding these mutually exclusive cases gives 1 + 5 + 10 = 16. Therefore, 16 elements of P(A) have at most two elements, so option C is correct. The count must include the empty set because zero is allowed.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
“At most 2” means the subset may contain 0, 1, or 2 elements. The numbers of such subsets are C(5,0)=1, C(5,1)=5, and C(5,2)=10. Adding these mutually exclusive cases gives 1 + 5 + 10 = 16. Therefore, 16 elements of P(A) have at most two elements, so option C is correct. The count must include the empty set because zero is allowed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
