Let \(A=\{1,2,3\}\) and \(B=\{3,4\}\). Find \(A\times B\) and Show It Graphically
Question
Let \[ A=\{1,2,3\} \] and \[ B=\{3,4\}. \] Find \[ A\times B \] and show it graphically.
Solution
The Cartesian product \(A\times B\) is the set of all ordered pairs \((a,b)\) where \[ a \in A \] and \[ b \in B. \]
Given:
\[ A=\{1,2,3\} \]
\[ B=\{3,4\} \]
Now form all possible ordered pairs:
\[ (1,3),\ (1,4),\ (2,3),\ (2,4),\ (3,3),\ (3,4) \]
Therefore,
\[ \boxed{A\times B=\{(1,3),\ (1,4),\ (2,3),\ (2,4),\ (3,3),\ (3,4)\}} \]