Past exam of the logic and set theory course of the University of Oxford / 2011 / A / 1 / b / i

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- Solution i

Solution

The following is a logical derivation using only A1, A2 and the modus ponens rule. The first two lines are assumptions:

1. 2. 3. 4. 5. 6. 7. α \to β β \to γ (β \to γ) \to (α \to (β \to γ)) α \to (β \to γ) (α \to (β \to γ)) \to ((α \to β) \to (α \to γ)) (α \to β) \to (α \to γ) α \to γ assumption, assumption, A1, MP (2, 3), A2, MP (4, 5), MP (1, 6) .

Thus

{α \to β, β \to γ} ⊢ α \to γ

.

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