1. Not finding help here? Sign up for a free 30min 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!

Proving an implication

  1. Mar 20, 2013 #1
    A: (p => ~q) ^ (p v q)
    B: ~p v q

    does A => B (A implies B) ?
    does B => A ( B implies A) ?

    I did the truth tables for each:

    A => B:
    http://www4c.wolframalpha.com/input/?i=((p+=>+NOT+q)+AND+(p+OR+q))+=>+(NOT+p+OR+q)

    B => A:
    http://www.wolframalpha.com/input/?i=(NOT+p+OR+q)+=>+((p+=>+NOT+q)+AND+(p+OR+q))+.

    for A to logically imply B or for B to logically imply A, does it need to be a tautology? Meaning if A=> B or B=> A , on the truth tables should it be All Ts? or should the final column of the truh table of A=> B or B => A resemble the truth table of an implication?
     
    Last edited: Mar 20, 2013
  2. jcsd
  3. Mar 20, 2013 #2

    Mark44

    Staff: Mentor

    For the implication A => B, the only False you can have is when A is True and B is False. For all other combinations of truth values for A and B, the implication is considered to be True.
    For the implication B => A, the only False you can have is when B is True and A is False. For all other combinations of truth values for B and A, the implication is considered to be True.
     
  4. Mar 20, 2013 #3
    So does A logically imply B? or does B logically implies A?
     
  5. Mar 20, 2013 #4

    Mark44

    Staff: Mentor

    Make a truth table with five columns, one each for p, q, (p => ~q) ^ (p v q), ~p v q, and ((p => ~q) ^ (p v q)) => ~p v q. You can say that A => B if the only false value you get in the fifth column is in the row where there's a T in the third column and an F in the fourth column.

    Similar idea for B => A.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proving an implication
Loading...