# Prove logical equivalence

1. Sep 11, 2015

### cashflow

I took a quiz that I was very confident in and just got the scores back today -- I did terribly (50%). Anyway, I am trying to understand where my mistake is below. I went over this three times and I cannot figure out why it's wrong (it looks right to me).

To Prove: ~(p ∧ r) ∨ ~(q ∨ r) ≡ p ∧ r → ~r ∧ ~q

First, we know that a ≡ b is the same as b ≡ a. So, in my case, I started with b and worked to prove a.

Proof:
Starting with:
p ∧ r → ~r ∧ ~q
≡ ~(p ∧ r) ∨ (~r ∧ ~q) by the '∨' def. of '→'
≡ ~(p ∧ r) ∨ ~(r ∨ q) by De Morgan's Law
≡ ~(p ∧ r) ∨ ~(q ∨ r) by Commutative Law

I asked the professor where, and he said "It doesn't matter where. I looked at it and saw this lacked quality." I don't understand. I proved that the two sides are the logically equivalent in 3 steps. Help please? Thank you!

2. Sep 11, 2015

### Staff: Mentor

His reponse is very vague and unhelpful. I don't see anything wrong with your work. I would advise going to see your professor during office hours and asking him what he means by "lacking quality" and where, specifically, he considers your proof to be incorrect. I

If you don't get a good explanation from him, you could make an appointment with the department head.

3. Sep 11, 2015

### StevieTNZ

Could you perhaps prove it using a truth table?