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 `p ^^ r `

`-= r ^^ p `

`-= (r ^^ p) vv (p ^^ p) `

`-= (r vv p) ^^ p ` by the distributive law

`-= (not not r vv not not p) ^^ p `

`-= not(not r ^^ not p) ^^ p `  by DeMorgans Law