Problem 3: Equivalence relation Let R be the relation on the set of ordered pairs of positive integers, such that ((a, b), (c, d)) R if and only if ad = bc. Show that R is an equivalance relation.

Problem 4: Partial ordering Let R be a relation on the set of people such that xRy if x and y are people, and x is older than y. Show that R is not a partial ordering.

Problem 5: Circular relation A relation R is said to be circular if aRb and bRC imply cRa. Show that R is reflexive and circular if and only if it is an equivalence relation.