Assume that F: A to B is a function and S, a subset of B, is a subset. Prove that f(f-1(S))= S intersected with f(A).
[ f(f-1)) is f and inverse of f]
If , may not even be defined! (As we may choose to be )Originally Posted by ummmm
Or have I missed something.
Of course I have missed something:
choose to be ,
then:
-the empty set.
Back to the problem:
(we need only consider the case where as the result holds trivally otherwise)
,
so if then and
and ,
i.e.
Now suppose then clearly
and so
hence:
RonL