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Show that {1, 2, 3} under multiplication modulo 4 is not a
Chapter 2, Problem 9E(choose chapter or problem)
QUESTION:
Show that {1, 2, 3} under multiplication modulo 4 is not a group but that {1, 2, 3, 4} under multiplication modulo 5 is a group.
Questions & Answers
QUESTION:
Show that {1, 2, 3} under multiplication modulo 4 is not a group but that {1, 2, 3, 4} under multiplication modulo 5 is a group.
ANSWER:Step 1 of 3
To find: under multiplication modulo is not a group but that under multiplication modulo is a group.
Condition of group are:
(1) Associativity: The operation is associative, that is for on set.
(2) Identity: The element in set such that for all on set.
(3) Inverses: For each element in set, there is an element in set such that .