Prove/disprove questions on equivalence relations and ordered sets

Question

1. If $R$ is an equivalence relation and a partial order over $A \neq \emptyset$ then every equivalence class contain at least one element.

2. If $(A,\le)$ an ordered set, and $a\in A$ is a single maximal element, then $a$ is the maximum.

3. If $(A,\le)$ an ordered set, and $a\in A$, $a$ is the maximum, then $a$ is a single maximal element.

1. It has to be true since every equivalence relation is reflexive (proof by contraposition).

2. I don't know if they meant total or partial order, so I'll suppose total order here, so we know that $a\le b$ or $b \le a$, suppose $a$ is the single maximum, there's no $b$ such that $a\le b$.

3. Here I'll suppose we have a partial order, so we have the set $\{1,2,3,4,6\}$ with the order $aRb: a|b$ so here we have a maximum 4 and 6, so there's no single maximum.