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I do not know where to start and how to correctly prove pls help 1a and 1b

Let f:A->B be a function between sets A and B. We can think of functions as input – output machines, where are you feed it an element of A and it spits back out an element of B. Given a subset S (subset) A, define

1. Let $f:A?B$ be a function between sets $A$ and $B$. We can think of functions as input-output machines, where you feed it an element of $A$ and it spits back out an element of $B$. Given a subset $S?A$, define $f(S)={y?B?there existsa?Ssuch thatf(a)=y}?B.$ (a) Given subsets $S_{1},S_{2}?A$, prove that $f(S_{1}?S_{2})=f(S_{1})?f(S_{2})$. (b) Is $f(S_{1}?S_{2})=f(S_{1})?f(S_{2})$ true? If so, provide a proof, and if not, give a counterexample.

Solution:- let y?f(S1?S2)?y=f(x) for some x?S1?S2 ?x?S1orx?S2 Now if x?S1?y?f(S1)?y?f(S1)?f(S2) similarly x?S2?y?f(S2)?y?f(S1)?f(S2)Hence in each