中南大学《离散数学》课件-第13章（英文版）.ppt

Copyright2007@byXuDezhi*证明(a)1～(?xp(x)∧Q(a))P2～?xp(x)∨～Q(a)T,1,E113?xP(x)→～Q(a)T,2,E14(b)1?x(P(x)∨Q(X))p2P(y)∨Q(y)T,1,US3?x～P(x)P4～P(y)T,3,US5Q(y)T,2,4,I56?xQ(x)T,5,UGCopyright2007@byXuDezhi*(c)1～?x(P(x)∨Q(x))P2?x～(P(x)∨Q(x))T,1,Q43～(P(y)∨Q(y))T,2,ES4～P(y)∧～Q(y)T,3,E105～P(y)T,4,I26?xP(x)P7P(y)T,6,US8P(y)∧～P(y)T,5,79～?xQ(x)T,8Copyright2007@byXuDezhi*Homework1Decidewhichargumentsarevalidandconstructpoofforthem.(a)A∧B(b)A∨BA→CA→C∴C∧B∴C∨B(c)A→B(d)A→B∨CA→CD→～C∴C→BB→～AAD∴B∧～BCopyright2007@byXuDezhi*Homework2IftodayisTue,thenIhaveaDMtestorphysicstest.Ifthephysicsteacherisill,thenthere’llbenophysicstest.TodayisTueandthephysicsteacherisill,therefore,IhaveaDMtest.Copyright2007@byXuDezhi*Homework3Showthat(a)～P∨Q,～Q∨R,R→S?P→S(b)P→Q?P→P∧Q(c)P∨Q→R?P∧Q→RCopyright2007@byXuDezhi*TheEndCopyright2007@byXuDezhi*1.1.1设P是命题“天下雪”；Q是命题“我去镇上”；R是命题“我有时间”。(a)用逻辑符号写出以下命题：(1)如果天下雪和我有时间，那么我去镇上。(2)我去镇上，仅当我有时间。(3)天不下雪。(4)天正在下雪，我也没有去镇上。(b)对下述命题用中文写出语句。(1)Q?(R∧～P)(2)R∧Q(3)(Q→R)∧(R→Q)(4)～(R∨Q)Copyright2007@byXuDezhi*解(a)(1)～P∧R→Q(2)Q→