Show that $((p \rightarrow q) \vee (p \rightarrow r))$ and $p \rightarrow (q \wedge r)$ are logically equivalent. Show that $((p \rightarrow q) \vee (p \rightarrow r))$ and $p \rightarrow (q \wedge r)$ are logically equivalent.  
I am wondering if my professor put the wrong symbol on our review guide because I have worked on this one over and over cannot logically explain 'p implies q or p implies r' being equal to 'p implies q and r'.  
Should the second argument be $p \rightarrow (q \vee r)$? Or is there a solution to my professor's question?

You are right. $p\implies r$ is the same logically as $p\wedge r\vee\neg p$. Therefore,
$(p\implies q)\vee (p\implies r)$ is the same as $(p\wedge q\vee\neg p)\vee(p\wedge r\vee\neg p)=p\wedge q\vee p\wedge r\vee\neg p=p\wedge (q\vee r)\vee\neg p$, which is the same as $p\implies q\vee r$, which is distinct from $p\implies q\wedge r$.
