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(e) Show that $\vdash \lnot(p \lor \lnot p) \to p \land \lnot p$

(f) Show that $\models p \lor \lnot p$ and $\vdash p \lor \lnot p$. For the second part, you can assume (e), i.e. you can treat $\lnot (p \lor \lnot p) \to p \land \lnot p$ as an assumption.

The first part is natural deduction, I just can't figure out how to go about it, and the second part I'm really not sure about.

Thank you

$$% I'll add a link because I'm not sure how to put the symbols. [https://imgur.com/a/ijaE1vQ][1] [1]: https://imgur.com/a/ijaE1vQ$$

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Hint

Assume $\lnot (p \lor \lnot p)$ and assume $p$. From it derive a contradiction and conclude with $\lnot p$ discharging the assumption.

Then assume $\lnot p$ and repeat, using double negation to conclude with $p$.

For $\vDash p \lor \lnot p$ use truth table.

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