logic - 如何演绎地证明以下逻辑语句？

Question

我有以下逻辑语句：

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

我被告知使用多萝西定律，即：

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

我无法弄清楚解决这个问题所需的确切推理规则和/或法律。谢谢。

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