let $R$ is a relation such that $R = \{(a,b) \in \Bbb Z_+^2: a \vert (b+1)\}$. Is this relation symmetric, reflexive and transitive?
The only problem i am facing is proving whether is it symmetric or not? this is what i am doing..
if $a\vert(b+1)$, then $b+1 = ka$ where $k$ is a constant.
And now i have to prove that $b\vert(a+1)$ which can be written as $a+1 = qb$ where $q$ is a constant.
Now am stuck what to do next. i considered $k$ and $q$ to be equals to $1$ just as an example which leads to $a = b+1$ and $b = a+1$ which is absurd, so that means relation is not symmetric?