1. a) Let S be an integer set. Prove that the law of multiplication defined by ab = a is associative. b) Assume that the

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answerhappygod
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1. a) Let S be an integer set. Prove that the law of multiplication defined by ab = a is associative. b) Assume that the

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1.
a) Let S be an integer set. Prove that the law of multiplicationdefined by ab = a is associative.
b) Assume that the equation xyz = 1 holds in a group G.Does it follow that yzx = 1? That yxz = 1? Justify your answer.
c) Assume that an element x of a group has order rs. Findthe order of xr
d) Assuming that x has arbitrary order n, what is the orderof xr?
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