Let $R$ be a relation on $\mathbb{N} \times \mathbb{N}$ defined by $(a,b)\, R\, (c,d)$ if and only if $ad(b-c) = bc(a-d)$. Then $R$ is\\
(1) symmetric but neither reflexive nor transitive\\
(2) transitive but neither reflexive nor symmetric\\
(3) reflexive and symmetric but not transitive\\
(4) symmetric and transitive but not reflexive