Question

Let $R$ be relation from $Q$ to $Q$ defined by $R=\left\{\right(a,b):a,b\in Qanda-b\in Z\}$.
Show that :
$(a,b)\in R$ implies that $(b,a)\in R$.

Answer 1

If $(a,b)\in R$

$\Rightarrow a-b$ is an integer, then $b-a$ would also be an integer being $-(a-b)$

$\Rightarrow b-a$ also $\in Z\Rightarrow (b,a)\in R$.