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# MAT301 Assigment 1 Self Generated Solutions Full Mark!

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Department
Mathematics
Course
MAT301H1
Professor
Fiona Murnaghan
Semester
Fall

Description
MA Assignment Let G x is a real number and -12 ab Va. E a deb Prove that Satisfies axiom CGIS Ga Prove PR or Lek a b be. any elements of G a, b e IR. want to show a b E ie. arb e're ans. a b e R is obvious because the set of all real numbers is closed under adok on an -mulh plication rtradicti prost b Need to sh e Suppose b tab o which is a Con traduction a C G reaye. to Let a btab b+ ab C, t atbtc tab a C be t ab MA Assignment Let G x is a real number and -12 ab Va. E a deb Prove that Satisfies axiom CGIS Ga Prove PR or Lek a b be. any elements of G a, b e IR. want to show a b E ie. arb e're ans. a b e R is obvious because the set of all real numbers is closed under adok on an -mulh plication rtradicti prost b Need to sh e Suppose b tab o which is a Con traduction a C G reaye. to Let a btab b+ ab C, t atbtc tab a C be t aba *(b b c a b a ve verified that ca brec a bt C) As, 2 is verified. G3 show that is Ane element, Let a e a A& O a a. a Gs is verified Let a e G we can show that b is defined wel a Also be R and b t -1 so beG a b a a a t a where is the identi element e haa shown that Ca )s a a D Lek G be a set that the fi Letwo owns a group namely GI and Gi If G also satisfies the two There a e G ks a Pra v PROor Tirst we want to how that the ngut inverse the t ha a e G because of verse (as we the inverse art the Same tw the left inverse we need to that the dent Let a E the the left inverse. a *(b b c a b a ve verified that ca brec a bt C) As, 2 is verified. G3 show that is Ane element, Let a e a A& O a a. a Gs is verified Let a e G we can show that b is defined wel a Also be R and b t -1 so beG a b a a a t a where is the identi element e haa shown that Ca )s a a D Lek G be a set that the fi Letwo owns a group namely GI and Gi If G also satisfies the two There a e G ks a Pra v PROor Tirst we want to how that the ngut inverse the t ha a e G because of verse (as we the inverse art the Same tw the left inverse we need to that the dent Let a E the the left inverse.We verified tuhod the N also proof the left which complet sek with lo
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