Let f A B be an arbitrary function and let X B and Y B be g

Let f : A B be an arbitrary function, and let X B and Y B be given. Prove that f1(X Y ) = f1(X) f1(Y ).

Solution

Let z f1(X Y )

f(z) ( X Y)

f(z) X and f(z) Y

z    f1(X)

z f1(Y)

z f1(X) f1(Y )

Let z f1(X) f1(Y )

z f1(X)

f(z) X

z f1(Y)

f(z) Y

f(z) X Y

z f1(X Y )