# Solutions to Intermediate Logic - pred./intuilistic logic/n. deduction/tableaux

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Question description

For revision purposes, I am desperate to have the solutions given and explained to the questions posed in the attached file. This is purely to widen my understanding of how these style of practice questions are answered.

Practice Exercises for Intermediate Logic (1) Give natural deduction proofs in classical predicate logic of the following: (a) ⊢NC ∀x(Fx ⊃ (Gx ⊃ Fx)) (b) ⊢NC ∀x(x = a ⊃ Fx) ⊃ Fa (2) Check the following using tableaux for modal predicate logic. Give a countermodel if the argument is invalid. (Make sure you explain why the interpretation you give ‘works’ as a countermodel) (a) ◇∃x ◻ Fx ⊢TCK ∃x ◇ ◻Fx (3) The following questions pertain to different proof systems for intuitionistic logic. (a) Check using tableaux. Give and explain a countermodel if invalid. ⊢TI (p ∧ (⇁p ∨ q)) ⊐ q (b) Prove using natural deduction. ⇁⇁⇁p ⊢NI⇁p (c) Use the Gödel translation and test using Kρτ tableaux. Give and explain a counter model if invalid. ⊧I⇁⇁(p∨ ⇁p) (4) Use the appropriate tableaux system to test each claim. Give a countermodel if the argument is invalid. (Make sure you explain why the interpretation you give ‘works’ as a countermodel) (a) (p ∧ q) ⊃ r ⊢TK3 (p ⊃ r) ∨ (q ⊃ r) (b) ⊢TLP (p ∧ (p ⊃ q)) ⊃ q (5) Give a semantic argument for the following two claims. (a) ⊧Ł3 p → (q → p) (b) p → q ⊧RM3 ¬q → ¬p

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