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Having trouble doing this In this problem you can use either the natural deduction system or...

Having trouble doing this

In this problem you can use either the natural deduction system or the Hilbert-style proof system

(a) Give a deduction. You may not use any meta-rules such as the Deduction Theorem or completeness.

\vdash (\alpha \rightarrow \neg\beta)\rightarrow(\beta \rightarrow \neg\alpha)

b) Give a deduction or show that a deduction exists, i.e. you may use meta-rules such as hypothetical syllogism or the deduction theorem (but not completeness.)

\vdash (\alpha \rightarrow (\alpha \rightarrow \beta)) \rightarrow (\alpha \rightarrow \beta)

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Answer #1

N)

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