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Problem 53: (Properties Of The Divides Relation)
Let $A=\mathbb{N}$. Given $a,b\in \mathbb{N}$, let's say that $a$ and $b$ are related by $\mathrm{R}$ if and only if $a$ divides $b$. So using symbols we can write $a\mathrm{R}b$ if and only if $a|b$ (if and only if $b$ is a multiple of $a$).
- Is $R$ reflexive? Remember to justify your answer, here and below.
- Is $R$ symmetric?
- Is $R$ transitive?
- Is $R$ antisymmetric?
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