If \(B=\{1,2,3\}\), Represent \(B\times B\) Graphically
Question
If \[ A=\{1,2,4\} \] and \[ B=\{1,2,3\}, \] represent the set \[ B\times B \] graphically.
Solution
The Cartesian product \(B\times B\) is the set of all ordered pairs \((b_1,b_2)\) where
\[ b_1\in B \]
and
\[ b_2\in B. \]
Given:
\[ B=\{1,2,3\} \]
Therefore,
\[ B\times B= \{ \]
\[ (1,1),(1,2),(1,3), \]
\[ (2,1),(2,2),(2,3), \]
\[ (3,1),(3,2),(3,3) \} \]