Given f : A C and g: B C If x A B, then f(x) and g(x) are defined. Also, f(x) =g(x) for all x A B. We can now divide the set A U B into 3 disjoint sets as AB, A B and BC. Any element y in A U B will be found either in AB or A B or BC. Define f U g: A U BC as f U g(y) = f(y), if y AB= g(y) if y BA = f(y) if y A B. Since f(y) = g(y), this is a function in which y is uniquely mapped onto a set C. Thus f g: A B C