True or False? Given any set X and given any function , and , if h is one-to-one and , then . Justify your answer.
Whether the given statement, “Given any set and given any functions if is one-to-one and then ” is true or false.
A function is said to be one-to-one function if the distinct elements in domain must be mapped with distinct elements in co-domain.
The given statement is true.
Since is a one-to-one function from .
So for every ,
Also, consider that .
Therefore for all in
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