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