If n(A)=5, how many elements of P(A) have at least 4 elements?
Answer and explanation
Correct answer: 6
A subset with at least four elements must have either exactly four elements or exactly five elements, since A itself has only five elements. The number of four-element subsets is C(5,4)=5, and the number of five-element subsets is C(5,5)=1. Adding them gives 5+1=6. Therefore P(A) has exactly six subsets with at least four elements, making option A correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A subset with at least four elements must have either exactly four elements or exactly five elements, since A itself has only five elements. The number of four-element subsets is C(5,4)=5, and the number of five-element subsets is C(5,5)=1. Adding them gives 5+1=6. Therefore P(A) has exactly six subsets with at least four elements, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
