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

Question

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

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Answer

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

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