Throughout the subject of reductions, I was wondering:
If we take $L_1 = \Sigma^* $ and $L_2 = \emptyset$, is $L_1 \leq L_2$? is $L_2 \leq L_1$?
What I mean is, Is there some sort of reduction between any of the two with the other one?
I tried this:
Let us try $L_2 \leq L_1$, we need to show that such a reduction exists. Suppose f(x) is that reduction function in which $x \in L_2$ iff $f(x) \in L_1$.
But there aren't any $x$ in $\emptyset = L_2$, does that show that such a reduction doesn't exist?