→ HHdelta :有雙號班的可以給我考題嗎?我想把它補齊 01/14 18:45
推 jacky2086 :大推 01/15 00:51
推 vffhhu :教授和助教人都超好的!!!大推~~~ 01/15 02:17
課程名稱︰基礎邏輯
課程性質︰哲學系必修
課程教師︰彭孟堯
開課學院：文學院
開課系所︰哲學系
考試日期（年月日）︰2010/01/14
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(註:請想像所有E都是左右相反的...它是存在命題)
*本次考試滿分105分。題目包括以下8題(佔95分)，以及你的助教的考題(佔10分)。請詳
細閱讀題目，審慎作答。
*以免影響他人考試，請將手機關機或者關至無聲。
I.下列論證是有效的，請使用推論規則證明(直接證法、條件證法、或反證法皆可，方法
不拘):
(1) 1.(x)(Px→~Qx) (15分)
2.PavPb/ (Ex)~Qx
(2) 1.(x)((~Px^Qx)→Rx) (15分)
2.(Ex)(Qx^~Sx)
3.(x)(Px→Sx)/ (Ex)Rx
(3) 1.~(Ex)Pxv(x)(Qx→Rx) (15分) (本題步驟較多)
2.(Ex)Sx→~(x)Rx
3.(Ex)(Px^Sx)/ (Ex)~Qx
II請用述詞邏輯的符號系統翻譯下列語句:
(4) 只有青竹絲和雨傘節是有毒的。 (10分)
(論域:蛇類。Px:x是青竹絲；Qx:x是雨傘節；Rx:x是有毒的)
(5) 鯨既不是魚類，也不是爬蟲類。 (10分)
(論域:動物類。Px:x是鯨；Qx:x是魚類；Rx:x是爬蟲類)
(6) 如果老張是邏輯學家，則他不但修過數理邏輯，也修過後設邏輯。
(a:老張；Px:x是邏輯學家；Qx:x修過數理邏輯；Rx:x修過後設邏輯) (10分)
III.下列論證是無效的，請以釋模法證明:
(7) 1.(x)(Px→Qx) (10分)
2.(Ex)~Px
/ (x)~Qx
(8) 1.(Ex)(Px→Qx) (10分)
2.(Ex)(Qx→Rx)
/ (Ex)(Px→Rx)
祝各位寒假愉快!
助教題
助教:林璿之
Elementary Logic Final Exam
You may choose any two of these questions, each one counts for five points.
1.Show that Γ,(φvψ)├ if and only if both Γ,φ├ and Γ,ψ├
2.Formalise the following argument and determine whether the argument is valid:
For any numbers,x,y,z if x>y and y>z, then x>z.
x>x is false for all numbers x.
Therefore, for any numbers x and y, if x>y, then it is not the case that y>x.
3.A wff is said to be logically valid if and only if φ is true for every
interpretation. A wff is said to be satisfiable if and only if there is an
interpretation for which φ is satisfied by at least one sequence.
(a) Find a satisfiable closed wff that is not true in any interpretation whose
domain has only one member.
(b) Find a satisfiable closed wff that is not true in any interpretation whose
domain has fewer than three members,
4.Explain the following terms:
(a) domain
(b) first-order logic (in terms of its alphabets and formation rules)
(c) equivalence relation
(d) scope
(e) an occurrence of a variable is free
5.Categorize the following binary relations by using notions of reflexivity,
symmetricity, transitivity.
(a) >
(b)≦
(c) =
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※ 編輯: HHdelta 來自: 140.112.4.191 (01/14 18:43)