Proving $f^{-1} (C) \backslash f^{-1} (D)= f^{-1} (C \backslash D)$ where $C,D \subseteq A$ and $E,F \subseteq B$ for $f: A \rightarrow B$

Asked Mar 29 '21 at 14:00

Active Mar 29 '21 at 14:05

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I do not understand how it is possible to use the domain of the function $f$ in the inverse function. I believe it should take numbers from the set $B$ in the inverse function, since it goes from $B \rightarrow A$

edited Mar 29 '21 at 14:05

asked Mar 29 '21 at 14:00

Sumsar

exactly. C and D must be inside B. Does this work for you: https://math.stackexchange.com/questions/1372833 – 311411 Mar 29 '21 at 14:08
Welcome! Here $f^{-1}$ is the pre-image, not the inverse I guess. Other than that yes, for sure $C, D$ should be subset of $B$. Very nice panda by the way:D – Bargabbiati Mar 29 '21 at 14:10

Proving $f^{-1} (C) \backslash f^{-1} (D)= f^{-1} (C \backslash D)$ where $C,D \subseteq A$ and $E,F \subseteq B$ for $f: A \rightarrow B$

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