Find the Total Number of Relations from \(A\) into \(B\)
Question
Let \[ A=\{1,2\} \] and \[ B=\{3,4\}. \]
Find the total number of relations from \(A\) into \(B\).
Solution
\[ n(A)=2,\quad n(B)=2 \]
Number of elements in \[ A\times B \] is
\[ n(A\times B)=2\times2=4 \]
Total number of relations from \(A\) into \(B\) is
\[ 2^{\,n(A\times B)} \]
\[ =2^4 \]
\[ =16 \]
Therefore,
\[ \boxed{16} \]