MATH 13 Study Guide - Final Guide: Surjective Function, Bijection, Equivalence Class
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Math 13 winter 2017 sample writing for final exam. Proof of : if b r[x y ] then, by the de nition of image, there is some a . X y such that (a, b) r. if a x then, since (a, b) r, the de nition of image tells us that b r[x]. Since r[x] r[x] r[y ], we conclude b r[x] r[y ]. If a y then, since (a, b) r, the de nition of image tells us that b r[y ]. R[y ] r[x] r[y ], we conclude b r[x] r[y ]. R[x y ] = b r[x] r[y ], and thereby the inclusion . If b r[y ] the argument is the same, but symmetricity of the argument. Proof of : assume b r[x] r[y ]. By the de nition of the inverse, ar 1b i bra for every a a and b b, and similarly for all relations.
