   Chapter 3.1, Problem 5TFE

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Textbook Problem
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# Label each of the following statements as either true or false.Let G be a group that is not abelian. Then x y ≠ y x for all x and y in G .

To determine

Whether the statement, “Let G be a group that is not abelian, then xyyx for all x and y in G” is true or false.

Explanation

Explanation:

In an abelian group, all pairs of the group elements commute. That is, if G is an abelian group then ab=ba for all a,b in G.

Let G be a non-abelian group such that x, y are in G.

Choose x=e (identity element)

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