Notes: p&r; ∴ ¬(¬r&¬q)&p Prove this argument using natural deduction. thank you in advance!

Wednesday, October 1, 2014

p&r; ∴ ¬(¬r&¬q)&p Prove this argument using natural deduction. thank you in advance!

We want to show that the two statements are logically equivalent. We proceed by starting with the given and using logically true steps ending with the conclusion:

Given $\displaystyle{p}\wedge{r}$

$\displaystyle\equiv{r}\wedge{p}$

$\displaystyle\equiv{\left({r}\wedge{p}\right)}\vee{\left({p}\wedge{p}\right)}$

$\displaystyle\equiv{\left({r}\vee{p}\right)}\wedge{p}$ by the distributive law

$\displaystyle\equiv{\left(\neg\neg{r}\vee\neg\neg{p}\right)}\wedge{p}$

$\displaystyle\equiv\neg{\left(\neg{r}\wedge\neg{p}\right)}\wedge{p}$ by DeMorgans Law

Notes

Wednesday, October 1, 2014

p&r; ∴ ¬(¬r&¬q)&p Prove this argument using natural deduction. thank you in advance!

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