(2) Let X be the set {1,2,3,4,5,6,7}, and define an operation on X to be multiplication modulo 8. (Notice we've left out
Posted: Tue Sep 07, 2021 7:09 am
(2) Let X be the set {1,2,3,4,5,6,7}, and define an operation on X to be multiplication modulo 8. (Notice we've left out zero.) Make a Cayley table for X with this operation. Is it closed (i.e. a binary operation)? Is X associative? Is there an identity element? Which elements have an inverse? Is X a group? (3) Do the same as the previous problem, but with the set {1, 2, 3, 4, 5,6}, and multiplication mod 7.