If \(A=\{1,2,3\}\), \(B=\{3,4\}\), \(C=\{4,5,6\}\), Find \(A\times(B\cup C)\)
Question
If \[ A=\{1,2,3\},\quad B=\{3,4\},\quad C=\{4,5,6\}, \] find \[ A\times(B\cup C). \]
Solution
\[ B\cup C=\{3,4,5,6\} \]
\[ A\times(B\cup C) = \{ (1,3),(1,4),(1,5),(1,6), (2,3),(2,4),(2,5),(2,6), (3,3),(3,4),(3,5),(3,6) \} \]
Therefore,
\[ \boxed{ A\times(B\cup C) = \{ (1,3),(1,4),(1,5),(1,6), (2,3),(2,4),(2,5),(2,6), (3,3),(3,4),(3,5),(3,6) \} } \]