Let X and Y be sets, and let A and B be any subsets of X.Determine if for all functions from X to Y, F(A-B) = F(A) - F(B) Justify your answer

intuition tells me no because the F(A-B) will have a different x values going to a different y values in Y than F(A) - F(B)

also,

the left side will have x values from X such that they are in $\displaystyle A \cap B^c$

whereas the right side would have x values from X such that they are in $\displaystyle A \cup B$

and clearly $\displaystyle A \cap B^c \neq A \cup B $