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Suppose that a is a mapping from a set S to itself and

Chapter 5, Problem 13E

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QUESTION: Problem 13E

Suppose that a is a mapping from a set S to itself and α(α(x)) = x for all x in S. Prove that a is one-to-one and onto.

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QUESTION: Problem 13E

Suppose that a is a mapping from a set S to itself and α(α(x)) = x for all x in S. Prove that a is one-to-one and onto.

ANSWER:

Step 1 of 2

Suppose is a mapping from a set to itself and for all in .

To prove that is one-one and onto.

Let us consider

Then, using the definition of ,

Thus,  showing that is one-one.

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