Thread: logical equivalences

~(p and q) = q or ((~p or r) and (~p or ~r))

Could anyone help me figure out how to show that these are equivalent using logical equivalences. I tried using De Morgans law on the RHS and simplifying it to the LHS but I keep getting (q or p) which is not equivalent to ~(p and q).

If both p and q are true, then the left-hand side is false, but the right-hand side is true. If you had ~q on the right, I think that would be correct.

So basically it was written wrong? Cuz i copied that question straight out of a powerpoint that I'm using to study so I know I didn't change how its written. If it was written wrong it would make sense why I can't figure it out... I've tried just about every manipulation I can think of.

I think so, but don't take my word for it. If this is an assignment, I would let the instructor know and ask what to do with it. But to do this you need to be (reasonably) sure that, as the problem is written, the two sides are not logically equivalent.

ok, cool. Thanx!

DeMorgan ~(p and q) and you get ~p v ~ q