Natural Deduction Problems

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Reference no: EM132381110

Natural Deduction Problems -

Problem 1 - Give derivations of the following:

1. ¬ (φ → ψ) → (φ Λ ¬ψ)

2. (φ → χ) ∨ (ψ → χ) from the assumption (φ Λ ψ) → χ.

Problem 2 - Prove Proposition: Γ is inconsistent iff Γ|- φ for every sentence φ.

Problem 3 - Prove that Γ|- ¬φ iff Γ U{φ} is inconsistent.

Problem 4 - Complete the proof of Theorem: (Soundness). If φ is derivable from the un-discharged assumptions Γ, then Γ |= φ.

Reference no: EM132381110

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