How many subsets does the set {1,2,3} have?
Answer 1:
\(2^{3}=8\)
Explanation:
The subsets of \({1,2,3}\) are:
\(\{\} \text { a.k.а. } \emptyset\) the empty set
\(\{1\},\{2\},\{3\}\)
\(\{1,2\},\{1,3\},\{2,3\}\)
\(\{1,2,3\}\)
making a total of \(8\) subsets. I guess you probably missed out the empty set or the whole set in your count. In general, a set with \(N\) elements has \(2^{N}\) subsets. This works when you get to infinite sets and their cardinal numbers too.
Answer 2:
\(2^{3}=8\) subsets.
Explanation:
The number of subsets can be calculated from the number of elements in the set.
Number of subsets = \(2^{n}\)
So if there are \(3\) elements as in this case, there are:
\(2^{3}=8\) subsets.
Remember that the empty (or null) set and the set itself are subsets.
For \(S=\{1,2,3\}\), the subsets are: