Properties Of The Less Than Or Equal To Relation

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Problem 60: (Properties Of The Less Than Or Equal To Relation)

Let $A=\mathbb{R}$. Given $a,b\in \mathbb{R}$, let's say that $a$ and $b$ are related by $\mathrm{R}$ if and only if $a$ is less than or equal to $b$. So using symbols we can write $a\mathrm{R}b$ if and only if $a\leq b$.

1. Is $\mathrm{R}$ reflexive? Remember to justify your answer, here and below.
2. Is $\mathrm{R}$ symmetric?
3. Is $\mathrm{R}$ transitive?
4. Is $\mathrm{R}$ antisymmetric?

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