Can you answer Letter E, no.1? D. Determine whether or not each of the following definitions of * given below does give a binaryoperation on the given set. In the event that * is not a binary operation, state whether condition1 (well definedness, condition 2 (closure property), or both of these conditions are violated.1.On Z*, define * by a * b = a/b2. On R- {0}, define * by a *b = abE. For each binary operation * defined on a set below, say whether or not * gives a group structureon the set. If no group results, give the axiom that does not hold.1. (R* , * ) where * is defined by a * b = ab2. (Z, * ) where * is define by a * b = a - b.F. Let a e G where G is a group. What shall you show to prove that a= q?

Apologies. We only answer one question at a time. We will answer question E, no. 1 as the exact one…

E. For each binary operation * defined on a set below, say whether or not * gives a group structure on the set. If no group results, give the axiom that does not hold. 1. (R* , * ) where * is defined by a * b = ab

E. For each binary operation * defined on a set below, say whether or not * gives a group structure on the set. If no group results, give the axiom that does not hold. 1. (R* , * ) where * is defined by a * b = ab

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 43E: Write out the elements of P(A) for the set A={ a,b,c }, and construct an addition table for P(A)...

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Question

Can you answer Letter E, no.1?

D. Determine whether or not each of the following definitions of * given below does give a binary
operation on the given set. In the event that * is not a binary operation, state whether condition
1 (well definedness, condition 2 (closure property), or both of these conditions are violated.
1.
On Z*, define * by a * b = a/b
2. On R- {0}, define * by a *b = ab
E. For each binary operation * defined on a set below, say whether or not * gives a group structure
on the set. If no group results, give the axiom that does not hold.
1. (R* , * ) where * is defined by a * b = ab
2. (Z, * ) where * is define by a * b = a - b.
F. Let a e G where G is a group. What shall you show to prove that a= q?

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