Example: - Show that the "greater than or equal" relation () is a partial ordering on the set of integers. R={(a,b)ab}foralla,b,Z R is reflexive, since a a for every integer a R is antisymmetric, if ab and ba, then a=b. R is transitive because ab and bc imply that ac. It follows that is a partial ordering on the set of integers and (Z,) is a poset. Question: Is the "divides" relation on Z+a partial ordering, poset (Z+,)? a bab= integer Question: Is the "divides" relation on Z a partial ordering, poset (Z,) ? Question: Is the "inclusion" relation on P(S) of S a partial ordering, poset (P(S),) ? Question: Are (Z,=),(Z,=) and (Z,)