   Chapter 1.3, Problem 4TFE

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Textbook Problem
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# Label each of the following statements as either true or false.Let f , g , and h be mappings from A into A such that f ∘ g = f ∘ h . Then g = h .

To determine

Whether the statement “g=h” is true or false where f, g, and h are mappings from A into A such that fg=fh.

Explanation

Consider the set A={0,y} and the provided mappings f, g, and h such that, f(x)=0, g(x)=0 and h(x)=x.

Then the mapping compositions are given by,

(fg)(x)=f(g(x))=f(0)=0</

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