Question

If $A=\{2,3\},B=\{4,5\},=\{5,6\},$

find $A\times (B\cup C)$

$A\times (B\cup C),(A\times B)\cup (A\times C)$

Answer 1

Given :$A=\{2,3\},B=\{4,5\},=\{5,6\}$

$B\cup C=\{4,5\}\cup \{5,6\}$

$\Rightarrow B\cup C=\{4,5,6\}$

$A\times (B\cup C)=\{2,3\}\times \{4,5,6\}$

$\therefore A\times (B\cup C)=\left\{\begin{array}{cc}(2,4),(2,5),(2,6),(3,4),& \\ (3,5),(3,6)& \end{array}\right\}$

$B\cap C=\{4,5\}\cap \{5,6\}$

$\Rightarrow B\cap C=\left\{5\right\}$

$A\times (B\cap C)=\{2,3\}\times \left\{5\right\}$

$\therefore A\times (B\cap C)=\left\{\right(2,5),(3,5\left)\right\}$

$A\times B=\{2,3\}\times \{4,5\}$

$\Rightarrow A\times B=\left\{\right(2,4),(2,5),(3,4),(3,5\left)\right\}$

$A\times C=\{2,3\}\times \{5,6\}$

$\Rightarrow A\times B=\left\{\right(2,5),(2,6),(3,5),(3,6\left)\right\}$

$(A\times B)\cup (A\times C)=\left\{\right(2,4),(2,5),(3,4),(3,5\left)\right\}$

$\cup \left\{\right(2,5),(2,6),(3,5),(3,6\left)\right\}$

$\therefore (A\times B)\cup (A\times C)$

$=\left\{\right(2,4),(2,5),(3,4),(3,5),(2,6),(3,6\left)\right\}$