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.

Show that $\vdash (\neg\,p\rightarrow\neg\, q) \rightarrow (q\rightarrow p)$ .

Worked-out solution

dubbele negatie-redeneerregel opdracht 1

Show that $\neg\,p\lor q\vdash p \rightarrow q$ .

Worked-out solution

dubbele negatie-redeneerregel opdracht 2

Of course, the derivation below is also correct.

dubbele negatie-redeneerregel opdracht 2

Show that $\neg(p\land q)\vdash \neg\,p \lor \neg\,q$ .

Worked-out solution

dubbele negatie-redeneerregel opdracht 3

Show that $\vdash \neg(p\rightarrow q)\rightarrow (p \land \neg\,q)$ .

Worked-out solution

Contractie- en dubbele negatie-eliminatieregels opdracht 4