Solution Found!
Suppose that a is a mapping from a set S to itself and
Chapter 5, Problem 13E(choose chapter or problem)
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.
Questions & Answers
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.