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Mathematik-Online problems:

Problem 950: Mappings and Operations on Sets

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given are sets $ A,B\neq \emptyset$, a map $ f:A\rightarrow B$ as well as the subsets $ U,V\subset A$ and $ X,Y\subset B$. Consider the following relations; either prove them or find a suitable counter-example respectively.
a) $ f(U\cup V)=f(U)\cup f(V)$ b) $ f(U\cap V)=f(U)\cap f(V)$
c) $ f^{-1}(X\cup Y)=f^{-1}(X)\cup f^{-1}(Y)$                  d) $ f^{-1}(X\cap Y)=f^{-1}(X)\cap f^{-1}(Y)$
(Authors: Wipper/Abele)
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  automatisch erstellt am 6.  2. 2018