Question

Using laws of logic, prove that
(Q^ notR) ) =>notP is logically equivalent to
(P ^ Q) ) => R

Answer 1

i dont like truth tables =/

Answer 2

(Q and not R) => not P
= not( (Q and not R) and not (not P))
= not( (Q and not R) and P)
= not ( (P and Q) and not R)
= (P and Q) => R

Answer 3

would it be a truth table though? i can do those no problem, but it says using laws of logic.... does that make a difference?

Answer 4

The important result you need, and I've used, is that

P => Q

is equivalent to

not (P and not Q)

Answer 5

one way to show two logical statements are equivalent is to show their truth tables are equivalent. thats just one way to do it though. James' argument is a lot shorter.

Answer 6

ok thanks very much guys!