Could someone please check my work?

Suppose f: A B. Let C, and Cz be subsets of A. Prove That f (c, ) uf (c2) s f (c, UC2 ). Ler y E f (c, ) uf (c2 ). => yEf ( c ) or yE f (c 2 ) -7 FX EC such That f ( x) = y or EXEC, such That f(x)= y = >Since XEC, or X E C2 - X E C , UC , 7 4 = f ( x) E f (c, UC) -> Since yef (c, ) of (la) and yet (G, UC). > F CC, ) U f ( C , ) = f ( c, UC2)