Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A
$\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$
List the ordered pairs of the equivalence relations induced by $\Pi_1$.
Draw the graph of the above equivalence relation.
Let $\Pi_2 = \left\{\left\{a\right\}, \left\{b\right\}, \left\{C\right\}, \left\{d\right\}\right\}$
$\Pi_3 = \left\{\left\{a, b, c, d\right\}\right\}$
and $\Pi_4 = \left\{\left\{a, b\right\}, \left\{c,d\right\}\right\}$
Draw a Poset diagram of the poset, $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
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