Help to understand material implication This question comes from from my algebra paper:
$(p \rightarrow q)$ is logically equivalent to ... (then four options are given). 
The module states that the correct option is $(\sim p \lor q)$. That is: 

$$(p\rightarrow q) \iff (\sim p \lor q )$$

but I could not understand this problem or the solution. Could anybody help me?

$p \to q$ is only logically false if $p$ is true and $q$ is false.  So if not-$p$ or $q$ (or both) are true, you do not have to worry about $p \to q$ being false.  On the other hand, if both are false, then that's the same as saying $p$ is true and $q$ is false (De Morgan's Law), so $p \to q$ is false.  Therefore, the two are logically equivalent.
