课程名称︰逻辑
课程性质︰A4通识
课程教师︰傅皓政
开课学院：无
开课系所︰无
考试日期（年月日）︰2019/11/4
考试时限（分钟）：
是否需发放奖励金：是
■请按题号顺序作答于答案卷上
试题 :
一、请建构命题逻辑语言(提示:包括符号与形构规则两个部分)。(10%)
(Construct a suitable language for propositional logic. Hint:two parts
involved,alphabets and formation rules)
二、请判断下列句式哪些是合宜的句式?哪些是不合宜的句式?(10%)
(Please determine which of the following sentences are well-formed formulae
and ill-formed ones.)
(a) XΛ→Y
(b) A↔((BＶC)→(B↔A))
(c) G↔(HＶK)↔G
(d) ┐PΛ
(e) PΛ┐QＶQ
(f) ((C┐D)Λ(E↔D))Λ┐D
(g) (L→M)→(N↔N)
(h) ┐AB↔C
(i) ┐W↔XＶY
(j) ┐┐S
三、请判断下列陈述的真假，并且分别以T与F代表“真”与“假”。(10%)
(Please judge the true and false of the following statements and use the
symbols“T”and“F”for true and false statements respectively.)
1.所有前提实际上为真的论证可能是无效论证。(An argument might be invalid in
the case of its premises are true.)
2.有些结论是恒真句的论证是无效论证。(An argument might be invalid in the
case of its conclusion is a tautology.)
3.前提与结论不一致的论证一定是有效论证。(An argument must be valid when its
conclusion is inconsistent with premises.)
4.结论为偶真句的论证一定是无效论证。(An argument must be invalid in the
case of its conclusion is a contingent sentence.)
5.无效论证的前提可能实际上为假。(If an argument is invalid, then it is
possible that all of its premises are actually false.)
6.前提实际上为假而且结论实际上为真的论证一定是无效论证。(An argument must
be invalid in the case of all its premises are actually true and the
7.所有前提与结论都是矛盾句的论证可能是无效论证。(An argument might be
invalid if all its premises and conclusion are contradictions.)
8.所有前提一致的论证一定是有效论证。(An argument must be valid in the case
of all its premises are consistent.)
9.前提实际上为真而且结论实际上为假的论证可能是有效论证。(An argument might
be valid when all its premises are actually true and the conclusion is
actually false.)
10.无效论证的所有前提一定是一致的。(All the premises of an argument must be
consistent if it is an invalid one.)
四、请以真值表法判断下列句是哪些是恒真句、矛盾句或是偶真句。注意:必须列出演算过
程。(15%)(Please use truth table method to show which of the following
formulae are tautology, contradiction, or contingent. Note: Computational
process is required.)
(a)((P→Q)ΛR)→((Q↔R)→((P→Q)ΛR))
(b) M↔(K→(M→L))
(c)┐(B→(BＶC))
五、请判断下列各题中的两个句式之间是蕴含或是等值关系。如果是蕴含关系，以φ╞ψ
　　表示；若为等值关系，则以╞φ←→ψ表示，必须列出演算过程。(15%)(Please use
the designate method to determine the semantic relation between the
following formulae. If the entailment relation holds then show them of the form
　　φ╞ψ. On the other hand, show them of the form ╞φ←→ψ if they are
　　equivalent. Computational process is required.)
(a) (┐M→┐N)→(N→M) ；MＶ┐M
(b) GＶ(H→H) ；GＶH
(c)(┐PΛ┐Q)Ｖ(┐QΛ┐R)；(PΛQ)Ｖ(QΛR)
六、请写出等值于真值表中语句φ的DNF及CNF。(10%)
(Please write the DNF and CNF wquivalent to the following formulaeφ)
(a)