課程名稱︰邏輯
課程性質︰A4通識
課程教師︰傅皓政
開課學院：無
開課系所︰無
考試日期（年月日）︰2019/11/4
考試時限（分鐘）：
是否需發放獎勵金：是
■請按題號順序作答於答案卷上
試題 :
一、請建構命題邏輯語言(提示:包括符號與形構規則兩個部分)。(10%)
(Construct a suitable language for propositional logic. Hint:two parts
involved,alphabets and formation rules)
二、請判斷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、請判斷下列陳述的真假，並且分別以T與F代表「真」與「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.所有前提實際上為真的論證可能是無效論證。(An argument might be invalid in
the case of its premises are true.)
2.有些結論是恆真句的論證是無效論證。(An argument might be invalid in the
case of its conclusion is a tautology.)
3.前提與結論不一致的論證一定是有效論證。(An argument must be valid when its
conclusion is inconsistent with premises.)
4.結論為偶真句的論證一定是無效論證。(An argument must be invalid in the
case of its conclusion is a contingent sentence.)
5.無效論證的前提可能實際上為假。(If an argument is invalid, then it is
possible that all of its premises are actually false.)
6.前提實際上為假而且結論實際上為真的論證一定是無效論證。(An argument must
be invalid in the case of all its premises are actually true and the
7.所有前提與結論都是矛盾句的論證可能是無效論證。(An argument might be
invalid if all its premises and conclusion are contradictions.)
8.所有前提一致的論證一定是有效論證。(An argument must be valid in the case
of all its premises are consistent.)
9.前提實際上為真而且結論實際上為假的論證可能是有效論證。(An argument might
be valid when all its premises are actually true and the conclusion is
actually false.)
10.無效論證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、請以真值表法判斷下列句是哪些是恆真句、矛盾句或是偶真句。注意:必須列出演算過
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、請判斷下列各題中的兩個句式之間是蘊含或是等值關係。如果是蘊含關係，以φ╞ψ
　　表示；若為等值關係，則以╞φ←→ψ表示，必須列出演算過程。(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、請寫出等值於真值表中語句φ的DNF及CNF。(10%)
(Please write the DNF and CNF wquivalent to the following formulaeφ)
(a)