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