Suppose is one—to—one.
a. Prove that for every subset .
b. Prove that for all subsets and in X, .
for any subset
The function is one-to-one function and .
The objective is to prove that for all subsets is one to one.
Need to show that .
Suppose that .
If is not in , then there is some element such that but this contradicts the fact that is one to one
for all subsets .
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