How can I prove the following logic statement deductively?

Question

I have the following logic statement:

If (P OR Q) and
   (P => Q) and
   (Q => P)
Then 
   (P AND Q)

I'm told to use Dorothy's Law, which is:

If (A => B)
Then (A OR B => B)

I can't figure out the exact rules of inference and/or laws needed to solve this. Thanks.

Answer 1

P => Q Therefore P OR Q => Q
Q => P Therefore Q OR P => P

Finally,

(P OR Q) AND (Q OR P)=( P AND (Q OR P)) OR (Q AND (Q OR P))
                     =((P AND Q) OR (P AND P))  OR ((Q AND Q) OR (Q AND P))
                     =(P AND Q) OR (Q AND P)
                     =P AND Q