Discrete Math proving logical equivalnces

[noced]

I know how to use truth tables to prove they areequivalent, 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))) arelogically equivalent:


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

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

 

[stapel]

I know how to use truth tables to prove they areequivalent, 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))) arelogically equivalent...

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

I don't know that there is just one "right" first step. This seems like a good start. Now, is there a rule for converting "and" statements to "or" statements? If so, where does that lead?

 

[noced]

I don't know that there is just one "right" first step. This seems like a good start. Now, is there a rule for converting "and" statements to "or" statements? If so, where does that lead? [/FONT][/COLOR]

De Morgan's law would change the "and" to "or" statements. Then I would have : (p implies not q) or (p implies r).

 

[stapel]

De Morgan's law would change the "and" to "or" statements. Then I would have : (p implies not q) or (p implies r).

You can't turn an "and" into an "or" simply by changing the "and" to an "or". The statements conjoined by the "and" have to change, too. So take another look at de Morgan.