Given A = 1, 2, 3 , B = 3, 4 , C = 4, 5, 6 , find (A ) (B ) - Vidyadip

Question

Given A = {1, 2, 3}, B = {3, 4}, C ={4, 5, 6}, find $(\text{A}\times\text{B})\cap(\text{B}\times\text{C})$

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Answer

We have,
A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
$\therefore$ A × B = {1, 2, 3} × {3, 4}
= {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
and B × C = {3, 4} × {4, 5, 6}
= {(3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}
$\therefore\ (\text{A}\times\text{B})\cap(\text{B}\times\text{C})=\{(3,4)\}$

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