Recognizing equivalence relations. About 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. (a) The domain is a group of people. Person x is related to person y under relation P if x and y have a common parent (i. e., x and y have the same biological mother or the same biological father or both). You can assume that there is at least one pair in the group, x and y, such that xPy.
(b) The domain is a group of people. Person x is related to person y under relation M if x and y have the same biological mother. You can assume that there is at least one pair in the group, x and y, such that xMy.
(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.