Determine whether the following mathematical systems are groups or not. If it's a group, explain why all four group conditions (closure, identity, inverses, associativity) are satisfied. Also, specify if the group is Abelian (commutative). If it's not a group, show at least one of the four group conditions that is not satisfied. a) The set of even whole numbers under addition. (Remember that the number 0 is even since it is a multiple of 2:0 = 2 x 0)

Q: 6. Give an example of two groups with 9 elements each which are not isomorphic to each other (and…

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Q: Determine all cyclic groups that have exactly two generators.

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A: Group table and a finite group G.

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Q: 4. a. Show that the set {0,1,2,3,4} together with the operation ®is a group b. Show that {0,1,2,3,4}…

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A: Consider the given expression: The objective is to show:

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Q: Given two examples of finite abelian groups

A: Require examples of finite abelian groups.