Let S be the set of all subsets of {1,2,3,4,5}, let z = {1,2,3}, and define XℛY to mean that X∩{1,3,5} = Y∩{1,3,5}.?
Update:
i apologize, the instructions for the questions "show that the given relation R is an equivalence relation on set S. Then describe the equivalence class containing the given element z in S, and determine the number of distinct equivalence classes of R
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Hint: X∩{1,3,5} = Y∩{1,3,5} is always true since the order doesn't matter. So every set is equivalent to every other set.
Go through the elements of what makes an equivalence relation and show they all hold.
Fine. But there is no question here!