# Relations and partitions

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

© BrainMass Inc. brainmass.com October 9, 2019, 9:17 pm ad1c9bdddfhttps://brainmass.com/math/recurrence-relation/relations-partitions-179754

#### Solution Preview

Please see the attached file.

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

Proof.

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.

$2.19