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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