Introductory Real AnalysisUniversity of Washington Math 327, Spring 2020 2020, Dr. F. Dos Reis Homework 1 – KeyExercise 1.Let (F,+·) and (G,+,·) be defined by F={a, b, c, d}andG={A, B, C} Their addition and multiplication tables: ForF: +abcdaabcdbbcdaccdabddabc·abcd aaaaa babcd cacac dadcb ForG: +ABCAABCBBCACCAB·ABC AAAA BABC CACB You can assume without proof that the addition and multiplication in (F,+,·) and in (G,+,·) are associative, commutative and distributive. We could prove the claim by reconsidering all the possible values forx1,x2, andx3 and prove that (x1+x2) +x3=x1+ (x2+x3),(x1·x2)·x3=x1·(x2·x3 ) x1+x2=x2+x1,x1·x2=x2·x 1 (x1+x2)·x3=x1·x3+x2·x 3 That would be 64 cases forFand 27 cases forG. It is not difficult but it is time consuming.
