For a function f , define the image of a set X to be the set f(X) = {y | y = f(x) for some x X}. Define the inverse image or preimage of a set Y to...
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# For a function f , define the image of a set X to be the set f(X) = {y | y = f(x) for some x ∈ X}.

Define the inverse image or preimage of a set Y to be the set f −1 (Y) = {x | f(x) ∈ Y}. Prove the following statements, in which A and B are sets. By doing so, you will show that inverse images preserve set operations, but images typically do not

]  a) First, suppose that x f 1 ( A B ) . Then, f ( x ) A B . By definition of union, then... View the full answer

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