Sun 5 Jun, 2016 11:16 pm
I have to use logical equivalences to prove that the following three formulas are equal:
a → (b → c),
(a ∧ b) → c,
(a → b) → (a → c)
I did the first two and got ¬a V ( ¬b V c) and (¬a V ¬b) V c, respectively, so they're equal through association of V. I'm having difficulty with the last formula though. I did implicit elimination three times and ended up with (a ∧ ¬b) V (¬a V c). I'm not sure how to continue from here, I've tried distribution so far but that didn't seem to work. Any advice or tips?
Have you written out the truth tables ?
If you examine the truth tables you will find that the expressions are equivalent since only the combination a=T, b=T, c=F will give an F in each case.