Question

State True or False for the following statement:
If $A=1,2,3,B=3,4andC=4,5,6,$then

$(A\times B)\cup (A\times C)=$${\{}_{(2,3),(2,4),(2,5),(2,6),}^{(1,3),(1,4),(1,5),(1,6),}\left\}\right\{(3,3),(3,4),(3,5),(3,6)\}$

Answer 1

Given: $A=1,2,3,B=3,4$ and $C=4,5,6$

Since $(A\times B)\cup (A\times C)=A\times (B\cap C)$

$B\cup C=\{3,4,5,6\}$

$(A\times B)\cup (A\times C)=\{1,2,3\}\times \{3,4,5,6\}$

$={\{}_{(2,3),(2,4),(2,5),(2,6),}^{(1,3),(1,4),(1,5),(1,6),}(3,3),(3,4),(3,5),(3,6)\}$

Hence, the given statement is true.