理則學練習26 範例 (取自梅子姐) - ஜ無限世界ஜ - udn部落格

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理則學練習26 範例 (取自梅子姐)

2008/05/23 15:27:04瀏覽266｜回應0｜推薦0

A-9 The product of 3 and 7 is 21.

以"p"表"the product of 3 and 7";以"t"表"21"

符號化：p=t

The sentence is an identity sentence.

B-6 (∃x)[(Wx&Lxj)&–(x=j)]

(∃x)[(x是女人&x愛Joan)&x不是Joan]

至少有一人x，x是女人且x愛Joan且x不是Joan

有不是Joan本人的女人愛Joan

C-8 Some persons love no one other than themselves.

有些人只愛自己

至少有一人x，x只愛自己

(∃x)(y)(Lxy⊃y=x)

D-8 "a=b&b=c, therefore a=c" is valid.

1. a=b&b=c

Premise

2. –(a=c)

Premise

3. (b=a&b=c)⊃c=a

I-2

4. a=b

1, Simp.

5. (a=a&a=b)⊃b=a

I-2

6. a=a

I-1

7. a=a&a=b

6,4, c.a.

8. b=a

5,7, M.P.

9. b=c

1, Simp

10. b=a&b=c

8,9, c.a.

11. c=a

3,10, M.P.

12. (c=c&c=a)⊃a=c

I-2

13. c=c

I-1

14. c=c&c=a

13,11 c.a.

15. a=c

12,14, M.P.

16. (a=c)&–(a=c)

15,2, c.a.

以歸謬證法證出矛盾，可知原論證有效。或以直接證法：

1. a=b&b=c

Premise

2. (b=a&b=c)⊃c=a

I-2

3. (a=a&a=b)⊃b=a

I-2

4. a=a

I-1

5. a=b

1, Simp

6. a=a&a=b

4,5, b=a

7. b=a

3,6, M.P.

8. b=c

1, Simp

9. b=a&b=c

7,8, c.a.

10. c=a

2,9, M.P.

11. (c=c&c=a)⊃a=c

I-2

12. c=c

I-1

13. c=c&c=a

12,10, c.a.

14. a=c

11,13, M.P.

論證有效

( 知識學習｜隨堂筆記 )

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