Question

这道离散数学题怎么做，跪求大神帮忙

这道离散数学题怎么做，跪求大神帮忙

Answer 1

(QR→S)[R→(P+S)]<==>(P→Q)→(R→S).
证:用P'表示非P.
P→Q=P'+Q,
所以(QR→S)[R→(P+S)]
=[（QR）'+S][R'+P+S]
=(Q'+R'+S)(R'+P+S)
=(Q'+R')(R'+P)+S
=PQ'+R'+S.
(P→Q)→(R→S)
=(P→Q)'+(R→S)
=(P'+Q)'+R'+S
=PQ'+R'+S.
所以命题成立。