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# hw23 - a = b has a unique solution y ∈ G Exercise 67 If G...

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Intro to Abstract Math Homework 23 Fall 2009 Due November 6 Exercise 66. Let ( G, * ) be a group and let a, b, c G . Prove the following statements. a. Left cancellation: If a * b = a * c then b = c . b. Right cancellation: If b * a = c * a then b = c . c. The equation a * x = b has a unique solution x G . d. The equation y
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Unformatted text preview: * a = b has a unique solution y ∈ G . Exercise 67. If ( G, * ) is a group, and a,b,c ∈ G , is it always true that a * b = c * a implies b = c ? Be sure to justify your response. Exercise 68. Is ( Z ,-) a group?...
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