Let A = {1, 2, 3, 4} and $\text{R}=\{(\text{a},\text{b}):\text{a}\in\text{A},\text{b}\in\text{A},\text{ a divides b}\}.$ Write R explicitly.
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Answer
We have,
A = {1, 2, 3, 4}
and, $\text{R}=\{(\text{a},\text{b})=\text{a}\in\text{A},\text{ b}\in\text{A},\text{ a}\text{ divides b}\}$
Now, $\frac{\text{a}}{\text{b}}$ stands for 'a divides b'. For the elements of the given sets, we find that $\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{2}{2},\frac{3}{3}\text{ and }\frac{4}{4}$
$\therefore\ \text{R}=\{(1,1),(1,2),(1,3),(1,4),(2,2),(2,4),(3,3),(4,4)\}$
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