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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316|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"",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&NxLax)

No number is larger than itself. 符號化為:  (x)(NxLxx)

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

1. (x)(Cx&NxLax)

Premise

2. (x)(NxLxx)

Premise

3. Ca&NaLaa

1, U.I.

4. NaLaa

2, U.I.

5. LaaNa

4,Contra.

6. Ca&NaNa

3,5,Chain arg.

7. (Ca&Na)Na

6, T.F.E

8. CaNaNa

7,DeM.

9. CaNa

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.

 

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