1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Prove logical equivalence

  1. Sep 11, 2015 #1
    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. jcsd
  3. Sep 11, 2015 #2

    Mark44

    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.
     
  4. Sep 11, 2015 #3
    Could you perhaps prove it using a truth table?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove logical equivalence
  1. Proving this (Replies: 13)

  2. Prove that (Replies: 1)

  3. Prove that (Replies: 2)

  4. Math and logic (Replies: 4)

Loading...