a. For each of the following, either show that G is a group with the given operation or list the properties of a group t

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A For Each Of The Following Either Show That G Is A Group With The Given Operation Or List The Properties Of A Group T 1 (182.24 KiB) Viewed 57 times

a. For each of the following, either show that G is a group with the given operation or list the properties of a group that it does not have: i. G = N; addition ii. G = Z; a.b=a+b-ab iii. G = {0,2,4,6}; addition in Zg iv. G = {4,8,12,16); multiplication in Z20 [6] b. For each of the following, show that G is a group using the operation of S4, and determine how many elements of g of G satisfy g² = e. i. G = {e, (12)(34), (13)(24), (14)(23)} ii. G = {e, (1234), (13)(24), (1432)} [4]