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f:A->B

C,C1,C2 are subsets of A and D,D1,D2 are subsets of B

(most of that is not needed for this part)

C (contained in) f-1[f(C)] (f-1, is f inverse. i got to learn symbols)

okay, my teacher always tells us we can use examples to help us understand it but we can't use examples to prove something. however he then proceeded to prove it with an example. which made it far too simple especially since it was the same one i chose and then chose not to use

I know if it's 1-1(injective) then it's going to be equal and not just contained in one directions

(i

__assume__to be a function then it must be surjective, but I'm still not sure if that's correct to say)

so something like f: X^2 for some X in C would work

i had something like C={-2,-1...3} so the inverse funtion would have {-3} and C

but i spent a long time and a lot of space because I was trying to make the proof a more general statement

So, is it possible to give a more general proof to show it is contained in and would imply that it's not equal without actually having to counter example it is not equal?

I was definitely thrown off since he goes out of his way to say not to use examples and then summed them up with simple examples