离散数学证明题：证明((Q∧R)-->S) ∧(R-->(P∨S))(R∧(P-->Q))-->S
2019-05-27
离散数学证明题：证明((Q∧R)-->S) ∧(R-->(P∨S))(R∧(P-->Q))-->S
优质解答
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.
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.