理則學練習24 範例 (取自梅子姐) - ஜ無限世界ஜ

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理則學練習24 範例 (取自梅子姐)

2008/04/30 19:05:57瀏覽319｜回應0｜推薦0

A-1

1.(x)(∃y)Hyxy

Premise

2.(∃x)–(∃y)Hyxy

Premise

3.–(∃y)Hyay

2. E.I. x/a

4.(∃y)Hyay

1. U.I. x/a

5.(∃y)Hyay&–(∃y)Hyay

3,4, c.a.

B-3

將論域設限在"人"，符號設定："Lxy":"x loves y"

Everyone loves someone.符號化為: (x)(∃y)Lxy

Someone loves someone.符號化為: (∃x)(∃y)Lxy

證明句二的否定與句一一同是否會導出矛盾;

1. (x)(∃y)Lxy

Premise

2. –(∃x)(∃y)Lxy

Premise

3. (x)(y)–Lxy

2, Q.E.

4. (∃y)Lay

1, U.I.

5. (y)–Lay

3, U.I.

6. Lab

4,E.I.

7. –Lab

5, U.I.

8, Lab&–Lab

6,7, c.a.

導出矛盾，可知若第一句為真，則第二句絕不會為假。句一為真則句二必真，因此句一蘊含句二。

C-8

符號設定："Infinity":"a"; "Lxy":"x is larger than y"; "Cx":"x is a countable"; "Nx":"x is a number"

Infinity is larger than any countable number. 符號化為: (x)(Cx&Nx⊃Lax)

No number is larger than itself. 符號化為: (x)(Nx⊃–Lxx)

So infinity is not a countable number.符號化為: ∴ –(Ca&Na)

1. (x)(Cx&Nx⊃Lax)

Premise

2. (x)(Nx⊃–Lxx)

Premise

3. Ca&Na⊃Laa

1, U.I.

4. Na⊃–Laa

2, U.I.

5. Laa⊃–Na

4,Contra.

6. Ca&Na⊃–Na

3,5,Chain arg.

7. –(Ca&Na)∨–Na

6, T.F.E

8. –Ca∨–Na∨–Na

7,DeM.

9. –Ca∨–Na

8, T.F.E.

10. –(Ca&Na)

9, DeM.

得證，此為有效論證

D-3.(z)–(x)–Kzx; (∃z)(x)–Kzx

1. (z)–(x)–Kzx

Premise

2. (∃z)(x)–Kzx

Premise

3. (z)(∃x)Kzx

1, Q.E.

4. (x)–Kax

2, E.I.

5. (∃x)Kax

3, U.I.

6. Kab

5, E.I.

7. –Kab

4, U.I.

8. Kab&–Kab

6,7, c.a.

( 知識學習｜隨堂筆記 )