Philosophy Now Forum

Hi guys,

I'm currently working through a textbook on First Order Logic and am now at proofs. I've done quite a few so far but am really struggling with these three questions and wondered if anyone could construct some proofs for these questions to help me out. I've linked a proof checker below that is really useful. I hope somebody can help! Thank you

a. ∀x(Jx → Kx), ∀x(Kx → Lx), ∀x(Lx → Jx) ⊢ ∀x(Jx ↔ Lx)

b. ∃xFx, ∃yGy, ¬∃x∃y¬x = y ⊢ ∃z(Fz ∧ Gz)

c. ∀x∀y∀z((Rxy ∧ Rxz) → y = z), ¬∃x∀y(¬Rxy ∨ ¬Fy) ⊢ ∀x∀y(Rxy → Fy)


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Hi Jamie,

You seem to have mistaken this for a forum where you will find competent mathematicians (ha ha!). Most of the contributors to this forum, like myself, are not familiar with formal logical notation. However, quite a few are familiar with the logic of set theory. Are you able to frame your questions in more natural-language terms?