Determine the number of ordered pairs (A,B), where A is a subset of B and is a subset of {1,2,...,n},
Number of pairs of subsets $(A,B)$ of $\{1,2,3,\dots, n\}$ such that $A\subseteq B$.
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combinatorics
elementary-set-theory
1 Answers
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For each element of $\{1,2,\dots ,n\}$ we have three options. Put it only in $B$, put it in both $A$ and $B$, or put it in neither of them.
So the answer is $3^n$.