我有以下逻辑陈述:
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)
我无法弄清楚解决此问题所需的推理和/或法律的确切规则。感谢。
答案 0 :(得分:2)
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