If \(A=\{l,m,n,o,p\}\), how many one-element subsets does \(A\) have?
Answer and explanation
Correct answer: 5
A one-element subset is also called a singleton set. Each of the five elements of \(A\) produces exactly one singleton subset: \(\{l\}\), \(\{m\}\), \(\{n\}\), \(\{o\}\), and \(\{p\}\). Therefore, there are five one-element subsets. Equivalently, the number of subsets containing exactly one element is \(\binom{5}{1}=5\). The value 32 is the total number of all subsets, not only singleton subsets.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
A one-element subset is also called a singleton set. Each of the five elements of \(A\) produces exactly one singleton subset: \(\{l\}\), \(\{m\}\), \(\{n\}\), \(\{o\}\), and \(\{p\}\). Therefore, there are five one-element subsets. Equivalently, the number of subsets containing exactly one element is \(\binom{5}{1}=5\). The value 32 is the total number of all subsets, not only singleton subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
