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!

Homework Help: Logical equivalence

  1. Sep 8, 2014 #1
    Hi, I have to prove the following logical equivalence using algebraic substitutions:

    (p v ~q) v ~q → (r v p) ∧ ~q ≡ ~r v q → (q v p) ∧ (~p v ~q)

    I've already done the truth table for this problem and proved they are logically equivalent but am not sure how to go about using algebraic substitution. The first step I did was changing the if then by using the definition of 'v' but get stuck where to go after that..
  2. jcsd
  3. Sep 12, 2014 #2


    User Avatar

    Staff: Mentor

    Hi psu12. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    You can replace the implication relation on each side, using this equivalence:

    x → y ⇔ ~x V y

    Then methodically simplify each side using De Morgan's theorems.
    Last edited by a moderator: May 6, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted