Propositional Logic: Natural deduction
Contradiction and double negation elimination rules: pencil-and-paper exercises (4 exercises)
First, attempt each exercise on your own, and then compare your answer with the worked-out solution.
Exercise 1 Show that \( \vdash (\neg\,p\rightarrow\neg\, q) \rightarrow (q\rightarrow p)\).
Worked-out solution
Exercise 2 Show that \( \neg\,p\lor q\vdash p \rightarrow q\).
Worked-out solution
Of course, the derivation below is also correct.
Exercise 3 Show that \( \neg(p\land q)\vdash \neg\,p \lor \neg\,q\).
Worked-out solution
Exercise 4 Show that \( \vdash \neg(p\rightarrow q)\rightarrow (p \land \neg\,q)\).
Worked-out solution
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