Determine whether each relation is an equivalence relation. justify your answer. if the relation is an equivalence relation, then describe the partition defined by the equivalence classes.

(c) the domain is a group of people. person x is related to person y under relation s if x is currently the spouse of person y. you can assume that there is no polygamy and that there is at least one person who is married to another person in the group.

(d) the domain is the set of all integers. xey if x + y is even. an integer z is even if z = 2k for some integer k.



(a)

the domain of the equivalence relation d is the set s:

s = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17}

for any x, y ∈ s, xdy if x has the same remainder as y when divided by 4. show the partition of s defined by the equivalence classes of d.