Sequences and Summations Proof (Pre-imaging)
Hey, could anyone give me some assistance on this proof?
Let f be a function from A to B. Let S and T be subsets of B. Show that
f-1(S U T) = f-1(S)U f-1(T).
Where the f to the negative one denote the pre-image or inverse image.
I think by comparing the inverse images of two subsets in a function we might be comparing if they are equivalent, but not sure.
This comes from the Basic Structures: Sets, Functions, Sequences, and Sums from Sequences and Summations chapter.