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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