1. ## Proving Logical Equivalences

I know how to use truth tables to prove they are equivalent, but how do I prove symbolically using the rules of logic?

Show that (p -> ((not q) and r)) and (not p or (not (r implies q))) are logically equivalent:

(I wrote out some of the symbols for keys that I do not have)

I have no idea what to do now. Any help would be appreciated! Thank you!

2. ## Re: Proving Logical Equivalences

What rules of logic do you know? For example do you know that "not (r implies q)" is equivalent to "r and (not q)"?

3. ## Re: Proving Logical Equivalences

I was using conditional statements where p implies (q and r) is equivalent to ( p implies q) and (p implies r)

I started with the left hand side:

p implies (not q and r)

conditional statement: (p implies not q) and (p implies r)

that is what I have so far. I don't even know if that is the right step.