Let R be a relation on N × N defined by: (a, b) R (c, d) +d=b+c f… - Vidyadip

Question

Let R be a relation on N × N defined by:
$(\text{a, b})\text{ R }(\text{c, d})\Leftrightarrow\text{a}+\text{d}=\text{b}+\text{c}$ for all $(\text{a, b}),(\text{c, d})\in\text{N}\times\text{N}$
Show that:
$(\text{a},\text{b})\text{ R }(\text{a, b})\text{ for all }(\text{a, b})\in\text{N}\times\text{N}$

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Answer

We have,
$(\text{a, b})\text{ R }(\text{c, d})\Leftrightarrow\text{a}+\text{d}=\text{b}+\text{c}$ for all $(\text{a, b}),(\text{c, d})\in\text{N}\times\text{N}$
We have,
$\text{a}+\text{b}=\text{b}+\text{a}\ \forall\text{ a, b}\in\text{N} $
$\therefore(\text{a, b})\text{ R }(\text{a, b} )\forall\text{ a, b}\in\text{N}$

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