I've got to solve a following problem.
f is a function like this . And two sets . I've got to figure out how are the following two sets related:
I got to here:
Can I assume through this that ? If so then how to correctly justify it?
So is the following proof correct?
So let's assume that set is defined like this , this means that and .
So let's take any such that , then
Since , this means that
So I have proven that , in other words
But is not a subset of which can be proven by a counterexample like the one above.
Is this right?