Question

Verify the following identities where A = {1, 2, 3, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}
$A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$

Answer 1

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

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

$A\cup B=\{1,2,3,4,5,6\}$

$A\cup C=\{1,2,3,4,5,6,7\}$

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

From (1) and (2);

Hence proved.