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For each of the following, show that the formula is derivable from the set as indicated. You may use anything

proved in the Week 5 Slides, such as the Deduction Theorem and Hypothetical Syllogism, and anything occurring earlier in this assignment or question. You may not use the Completeness Theorem.

(a) For any formulas φ, ψ and γ, {ψ, (φ → (ψ → γ))} ⊢ (φ → γ).

(b) For any formulas φ, ψ and γ,

{(φ → (ψ → γ))} ⊢ (ψ → (φ → γ)).

(c) For propositional variables P, Q and R, {(P →Q),(¬R→¬Q)}⊢(P →R).

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