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