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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Let S be a nonempty finite set with a binary operation * that satisfies the associative law.
Show that S is a group if a * 6
= a *c implies b
= c and a * c = b*c implies a =
b for all
a, b, c E S. What can you say if S is infinite?
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- Let's consider a group G with the operation * defined as follows: For any two elements a, b in G, a * b = 2a + 3b. Given that G = {1, 2, 3, 4, 5} and the operation * is associative, find the identity element e in the group G.arrow_forwardFor each binary operation * defined on a set below, determine whether or not * gives a group structure on the set. If it is a group, explain why it is a group. If it is not a group, say which axioms fail to hold: (a) Define * on Z by a * b max(a, b). (b) Define * on Q \ {0} by a * b = |ab|. (c) Define * on Q+ by a * b = ab.arrow_forwardDetermine whether the set G is a group under the operation * G={n integer|n is odd}; a*b=a+barrow_forward
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