In Strang's Wavelets and Filter Banks, Problem 1.3.6 asks,
If $H_0$ is the response of a lowpass filter, what is the response $H_1$ of a corresponding highpass filter? If $h(0), \dots, h(N)$ are coefficients of $H_0$, what are the coefficients of your $H_1$?
I have gone through the section several times, and all I can find, as defining feature of lowpass and highpass filter, is the frequency response function being $1$ (and $0$) at frequency $0$, and $0$ (and $1$ respectively) at frequency $\pi$. These features do not reference one another, i.e., there is no clear definition of a "pair" of filters. I do not see any defining relationship between the two of a pair anywhere in this section. What am I missing here?