Let f : A→B and g : C→D be functions. The product of f and g is the function defined as follows:<BR>[f＊g](x,y)=(f(x),g(y)) for every (x,y)∈A X C<BR><BR>Prove that f*g is a function from A X C to B X D. <BR>Prove that if f and g are injective, then f*g is injective and if f and g are surjective, then f*g is surjective. <BR>Prove that ran[f*g]=(ranf)X(rang)<BR><BR>음...저희 과 동기들을 보니까 다 어설프게?? 증명을 하더군요..100점 만점에 70점 정도? 전 제대로된 논리적인 증명을 원하는데 감을 잘 못잡겠습니다.<BR><BR>
