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