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