1. The problem statement, all variables and given/known data
Let f : X to Y . For each element b element of Y , let Y_b = f^1({b}). Prove that the Y_b's
have the following property:
(a) If b and c are distinct elements of Y , then Yb intersection Yc = ∅.
(b) X =U_element of Y ( Yb).
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2. Relevant equations
3. The attempt at a solution
Well a) we know that b≠c, but we have to prove that Y_b n Y_c is an empty set. I know it have to be an empty set becase Y_b=f^1({b}) and Y_c=f^1({c}); so it Y_b n Y_c would not be empty then f is not a function. But I don't know how to prove it.
b) X is a union of Y_b  I have no idea how to even start. I submitted pdf file.
