Question

离散数学证明题：证明((Q∧R)-->S) ∧(R-->(P∨S))<=>(R∧(P-->Q))-->S 求解！

Answer 1

左边: ((Q∧R)→S)∧(R→(PvS)) = (┐(Q∧R)vS)∧(┐Rv(PvS))
= (┐Q v ┐R v S)∧(┐R v P v S)
右边: (R∧(P→Q))→S = ┐(R∧(┐PvQ))v S = (┐R v (P∧┐Q) v S )
= ((┐RvP)∧(┐R v ┐Q))v S = (┐R v P v S)∧(┐R v ┐Q v S)

((Q∧R)→S)∧(R→(PvS))<=> (R∧(P→Q))→S得证。