4. a. Define the following Terms giving one example each: i. Partial Ordering Relations ii. Equivalence relations b. Answer these questions for the partial order represented by the following Hasse diagram. a d' i m k n h i. Find the maximal elements. ii. Find the minimal elements. iii. Is there a greatest element? iv. Is there a least element? v. Find all upper bounds of {m, k, s}. vi. Find all lower bounds of {c, d, t}. vii. Find the greatest lower bound of {u, k, m} if it exists. viii. Find the least upper bound of {b, k, t} if it exists.

Draw the Hasse diagram for the following partial order.

Question Number 07 a) Determine whether the relation with the directed graph shown is an equivalence relation. b) Determine whether the relation represented by the zero-one matrix is a poset (partial order set): [1 1 1] Lo 1.