The Answer to the Question
is below this banner.
Here's the Solution to this Question
Let , and
(a) By defenition, a partition of a set is a set of non-empty subsets of such that every element in is in exactly one of these subsets. Since are non-empty set and each element is in exactly one of the sets and , really is a partiton of .
(b) Let us find the equivalence relation on induced by . By defenition, if and only if and are elements of the same set of a partition. In our case,