using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11.

P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x))

P6: ∀x∀y∀z((StrongPref(x,y)∧StrongPref(y,z))→StrongPref(x,z))

P7: ∀xIndiff(x,x)

P8: ∀x∀y(Indiff(x,y)→Indiff(y,x))

P9: ∀x∀y∀z((StrongPref(x,y)∧Indiff(y,z))→StrongPref(x,z))

P10: ∀x∀y(StrongPref(x,y)∨Indiff(x,y)∨StrongPref(y,x))

P11: ∀x∀y(WeakPref(x,y)↔(StrongPref(x,y)∨Indiff(x,y)))

C7: ∀x∀y∀z((StrongPref(x,y)∧StrongPref(y,z))→StrongPref(x,z))

C7 is totally the same as P6? So that means I can't use P6?

  • Yes C7 is the same as Premise6. – Mauro ALLEGRANZA Apr 7 '20 at 10:22
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    Thus, assuming that the text of the problem is correct, you have a one-line only proof. – Mauro ALLEGRANZA Apr 7 '20 at 11:59
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