PROBLEM 8 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 z is related to person y under relation M if z and y have the same favorite color. You can assume that there is at least one pair in the group, z and y, such that xMy. (b) The domain is the set of all integers. zEy if x + y is even. An integer z is even if z = 2k for some integer k.

Question
PROBLEM 8
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 z is related to person y under
relation M if z and y have the same favorite color. You can assume that
there is at least one pair in the group, z and y, such that xMy.
(b) The domain is the set of all integers. zEy if x + y is even. An integer z is
even if z = 2k for some integer k.
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PROBLEM 8 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 z is related to person y under relation M if z and y have the same favorite color. You can assume that there is at least one pair in the group, z and y, such that xMy. (b) The domain is the set of all integers. zEy if x + y is even. An integer z is even if z = 2k for some integer k.

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