Is the following sentence a tautology: $(p\Rightarrow q)\vee(r \Rightarrow p)\vee(r\Rightarrow s)\vee(r\Rightarrow q)$? If both $p$ and $q$ are false then ($p\Rightarrow q$) is true.
If either $p$ or $q$ is true  then one of ($r\Rightarrow p$) or ($r\Rightarrow q$) is true.
If both $p$ and $q$ are true then all are true.
Since they are OR'ed, one way of an other is true.
IT IS A TAUTOLOGY..
My prof dint accept my answer, he said need little more consideration.

$p \Rightarrow q$ is equivalent to $\neg p \lor q$.  So $(p\Rightarrow q)\vee(r \Rightarrow p)\vee(r\Rightarrow s)\vee(r\Rightarrow q)$ is equivalent to $(\neg p \lor q) \lor (\neg r \lor p) \lor (\text{others})$ which is equivalent to $\neg p \lor p \lor (\text{others})$ which is equivalent to $\top$.
