If $f$ reduces $L_1$ to $L$ and also $L_2$ to $L$ is $L_1=L_2$ If the same $f$ reduces $L_1$ to $L$ and also $L_2$ to $L$ does it imply that $L_1=L_2$?
My intuition says no, but I couldn't find a counterexample.
Using the definition of reduction,
$x\in L_1\iff f(x)\in L \iff x\in L_2$
And thus $L_1=L_2$.