The question I'm stuck on is:
Let $p$ and $q$ be propositions. A compound proposition $f(p,q)$ is given by $(p\vee \neg q) \Rightarrow (p \Leftrightarrow q)$. Find two non-equivalent propositions $h_1(q)$ and $h_2(q)$ which depend only on $q$, such that both propositions $f(p,q)\vee h_1(q)$ and $f(p,q)\vee h_2(q)$ are tautologies.
I have completed the truth table for the original proposition and have ended up with (T F T T) with both $p$ and $q$; but I'm unsure how to find a proposition where only $q$ is a variable (from what I know there are $4$ nonequivalent propositions for a single variable, I'm just not sure how to combine this information, or whether its right).