The following exercise is taken from Chapter 17 of Languages and Machines by Thomas Sudkamp:
Let $Q$ be a language reducible to a language $L$ in polynomial time. Prove that $\overline{Q}$ is reducible to $\overline{L}$ in polynomial time.
I am not sure if my solution idea is correct. Anyone knows the correct solution of this exercise?
My idea is: I use the definition of NP-complete. Q is in NP class and L is NP-complete. The function f to reducible in polynomial time Q to L, is also the function f to reducible in polynomial time notQ to notL