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: $(\text{a},\text{b})\text{ R }(\text{c, d})\text{ and (c, d) R (e, f)}$ $\Rightarrow(\text{a, b})\text{ R (e, f)}$ for all $(\text{a, b}),(\text{c, d}),(\text{e, f})\in\text{N}\times\text{N}$