Question

If $A=\{x:x^2–5x+6=0\},B=\{2,4\},C=\{4,5\}$, then $A\times (B\cap C)$ is

Answer 1

The value of $A\times (B\cap C)$ is

Given $A=\{x:x^2–5x+6=0\},B=\{2,4\},C=\{4,5\}$

$$\begin{gathered} \Rightarrow x^2–5x+6=0 \\ \Rightarrow x^2–3x–2x+6=0 \\ \Rightarrow x(x–3)–2(x–3)=0 \\ x=3,2 \\ A=\{3,2\}, \\ B=\{2,4\}, \\ C=\{4,5\} \\ A\times (B\cap C)=3x2x4 \\ =\{(2,4),(3,4)\} \end{gathered}$$

Hence the value of $\mathit{A}\mathbf{\times }\mathbf{(}\mathit{B}\mathbf{\cap }\mathit{C}\mathbf{)}$ is $\mathbf{\{}\mathbf{}\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{4}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{)}\mathbf{}\mathbf{\}}$.