MTH 421 Study Guide - Midterm Guide: Equivalence Class, Abstract Algebra, Surjective Function
Document Summary
Practice for exam - introduction to abstract algebra. The goal of this worksheet is to solidify concepts about sets, functions, equiva- lence relations and quotient sets. English is strongly encouraged as the language to use :) A = {1, 2, 3, 4, 5, joe, apple}, b = {1, 2, bob, joe}. A bc: true or false let. A = {1, 2, 3, 4, 5}, b = {1, 2, 5}, c = {10, 20, 30, 40, 50}. (a) (b) (c) (d) B c c: prove that for every pair of sets x and y , X x y: prove that two sets are equal if and only if they are each a subset of the other. Describe f g and g f: prove that the composition of two injective functions is an injective func- tion, and that the composition of two surjective functions is surjective. if f g is injective(resp. surjective),
