More First Order Logic Questions

For each problem below, provide a derivation of the conclusion from the premises using the rules of natural deduction (Simp, Adj, MTP, Add, MP, MT, DN, BI, BE, CI, and RAA) and the four rules in first order logic (UI, EG, UD and EI).

  1. ∃xFx & ∀xGx, ∀x(Fx –> Hx) ∴ ∃x(Gx & Hx)
  2. ∀x(Fx & Gx), Ga –> Hb ∴ Fc & Hb
  3. ∃xFx –> Ha, Fb, ∀x(Gx <–> Hx) ∴ ∃yGy
  4. ∀x∀y(Fxy <–> Gxy), ∀x∃yGxy, ∃x∃yFxy –> Hbc ∴ Hbc
  5. ∀x(Fx v Gx), ~Ga & ∀xHx, ∃x(Fx & Hx) –> Kc ∴ ∃xKx
  6. ∀x∃y(Fxy –> Gy), ∀x~Gx ∴ ∃x(~Fcx v Hx)
  7. ∀x(∃yFy –> (Gx v Hx)), Fc & ~Ha ∴ ∃x(Gx v Kx)
  8. ∀x(Fx –> (Gx v ~∃yHy)), ∃xGx –> Ka, Hb ∴ ∀x(Fx –> ∃yKy)
  9. ~(∀x∀y(Fx –> Gy)) –> ~∃xHx, ∀x(Fx & Hx) ∴ (Hc & Gd) v ∃x(Kx & Fx)
  10. ∀x(Gx v Hx), ∀x(∀y(Fy & Ky) <–> Hx), ~Fa ∴ Gc

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Elementary Formal Logic Copyright © 2020 by Jenna Woodrow and Craig DeLancey is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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