Prove that if

g: A -> B is 1-1

f: B -> C is 1-1

then fog: A -> C is 1-1

pf.

Need to show that if f(g(a)) = f(g(c)) then a = c for fog to be 1-1

Because g is 1-1, g(a) = g(b) and a = b

Because f is 1-1, f(b) = f(c) and b = c therefore a = c

Therefore since a = c, fog is a 1-1 function.