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hugo28
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Show/Prove that if f: X → Y is one-to-one on X, and A subset of X, then f^-1(f(A))<= subset A.
If you wouldn’t mind, please check whether I did it correctly. Thanks in advance.
Suppose x Є A
Then, f(x) Є f(A)
By image function y =f(x)
Thus, y = f(x) Є f(A)
And by inverse image, f^-1(y) = f-1(f(x)) Є f^-1(f(A)) <= subset A
Therefore: Є f^-1(f(A)) <= subset A.
If you wouldn’t mind, please check whether I did it correctly. Thanks in advance.
Suppose x Є A
Then, f(x) Є f(A)
By image function y =f(x)
Thus, y = f(x) Є f(A)
And by inverse image, f^-1(y) = f-1(f(x)) Є f^-1(f(A)) <= subset A
Therefore: Є f^-1(f(A)) <= subset A.
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