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Relations and partitions

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College level proof before real analysis. Please see the attached file.

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Please see the attached file.

(Please solve for everything and show each step of your solution).


1. To show that R is an equivalence relation of the power set of S. We need to show that R is
(a) Reflexive: For any
Proof: For any is true trivially, as A and A have the same size.

(b) Symmetric: For any if then
Proof: Since , A and B have the same size. So, B ...

Solution Summary

The solution shows equivalent relations and describes partitions.