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!

Truth tables and implications

  1. Sep 8, 2011 #1
    1. The problem statement, all variables and given/known data
    For statements P, Q, and R, use a truth table to show that each of the following pairs of statements are logically equivalent.
    a) (P^Q) <=> P and P=>Q
    b) P=>(Q v R) and (~Q)=>(~P v R)

    screen_capture.jpg

    3. The attempt at a solution
    See attached truth tables.
    Basically, I have no idea how to correlate P and QvR in the table. If P is false or QvR is true, then the implication is true; I know that. I know P can only have 2 values, true or false, but QvR is only false under one condition. So, is P true or false in that slot? I can't figure out how to make the table, though.
    With the second table in b, I know how Q and not Q (~Q) relate, but cant see how to relate ~Q with (~PvR). If ~Q is false or (~PvR) is true, the implication is true. Again, I know how the implication works. It's this truth table that is making this problem vastly more difficult than it needs to be. Any help on filling them out is greatly appreciated.
     
  2. jcsd
  3. Sep 8, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Do you have to fill them out in 4 rows?? That's weird.

    The way I would handle it is to regard 8 possibilities:

    P Q R
    F F F
    F F T
    F T F
    F T T
    T F F
    T F T
    T T F
    T T T

    and fill in the rest.
     
  4. Sep 8, 2011 #3
    Micro, you have came to rescue on a few of these problems for me. I really appreciate it. I don't think I have to fill it out in the way I did, but I was following the example in my book. None of them had three variables. Your method seems like the best. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Truth tables and implications
  1. Truth tables (Replies: 6)

  2. Truth Tables (Replies: 1)

  3. Truth Tables (Replies: 5)

Loading...