Let $R$ be a relation on $\Bbb N$ defined by $(x, y) ∈ R$ iff there is a prime $p$ such that $y = px$. Describe in words the reflexive, symmetric and transitive closures of $R$, denoted by $r$, $s$ and $t$, respectively.
(a) What is the smallest partial order containing $R$?
(b) Using the reflexive, symmetric, and transitive closures, express the smallest equivalence relation containing an arbitrary relation.
I have tried to approach this problem many ways, but I cannot figure it out. How can I solve this?