How can I prove $P \rightarrow (Q \rightarrow R)$ is equivalent to $(P \wedge Q) \rightarrow R$ I'm a freshman CS student at my university and i'm struggling with understanding my professor through his thick accent. I've asked him to explain the proof for this multiple times and still have trouble comprehending what he's trying to tell me.

The question is: 

Prove that:  $P\rightarrow(Q\rightarrow R)$ is equivalent to $(P \wedge Q) \rightarrow R$

He wants us to prove it using math and goes on to tell me that $P \rightarrow (Q \rightarrow R) = \neg P \vee (\neg Q \vee R)$

From that point on, I was completely lost and unable to follow along.
You could just construct the truth tables for the two formulas: there are only three variables, so the tables are only eight lines.
Use de Morgan's laws, distributivity and so on to rearrange one formula into the other.
Use similar techniques to show that $[P\rightarrow (Q\rightarrow R)] \leftrightarrow [(P\wedge Q)\to R]$ is equivalent to true.
Use similar techniques to show that $[P\rightarrow (Q\rightarrow R)] \leftrightarrow \neg[(P\wedge Q)\rightarrow R]$ is equivalent to false.
Use one of the various propositional proof systems to accomplish one of 2&ndash;4, though that sort of thing will probably come up later in your course.