Q11

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, $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.