Question

Given : A = {2, 3}, B = {4, 5}, C = {5, 6}, then prove the following :
$(A\times B)\cup (B\times C)$ = {(2, 4), (2, 5), (3, 4), (3, 5)} $\cup$ {(4, 5), (4, 6), (5, 5), (5, 6)} = All the ordered pairs as they are disjoint.

Answer 1

$A=(2,3\};$ $B=(4,5\};$ $C=(5,6\}$

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

$(B\times C)=\left(\right(4,5),(4,6),(5,5),(5,6\left)\right\}$

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

Hence all the ordered pairs are disjoint.