Thursday, 4 March 2021

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, III, 8 p. 448

The only person who ordered fish is Astrid. The only person who suffered indigestion is Ms Wilson. Some person who ordered fish also suffered indigestion. Therefore, Astrid is Ms Wilson. (Px: x is a person; Ox: x ordered fish; Sx: x suffered indigestion; a: Astrid; w: Ms Wilson)

1.     Pa • Oa • (x)[(Px • Ox) ⊃ x = a]

2.     Pw • Sw • (x)[(Px • Sx) ⊃ x = w]

3.     (∃x)(Px • Ox • Sx)

∴ a = w

4.     Pr • Or • Sr

5.     (x)[(Px • Ox) ⊃ x = a] • Pa • Oa

6.     (x)[(Px • Ox) ⊃ x = a]

7.     (Pr • Or) ⊃ r = a

8.     (x)[(Px • Sx) ⊃ x = w] • Pw • Sw

9.     (x)[(Px • Sx) ⊃ x = w]

10. (Pr • Sr) ⊃ r = w

11. Pr • Or

12. r = a

13. Pr • Sr • Or

14. Pr • Sr

15. r = w

16. a = r

17. a = w

 

 

 

 

3 EI

1 Com

5 Simp

6 UI

2 Com

8 Simp

9 UI

4 Simp

7,11 MP

4 Com

13 Simp

10,14 MP

12 Id

15,16 Id


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