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 (validity)

  1. Oct 27, 2015 #1
    I want to use truth tables to show that equations can be satisfied or not, or if they are valid.

    not(X→(Y→X))

    (X∧(notX→notY))→Y

    I would say the first one is valid, because of the not in front of it, it's always true. I don't know about the second one. I don't know how to split them up best to use a truth table. I guess I can/should use:

    X, notX, notY, Y, X∧(notX→notY), notX→notY and (X∧(notX→notY))→Y.
     
  2. jcsd
  3. Oct 27, 2015 #2

    Geofleur

    User Avatar
    Science Advisor
    Gold Member

    Here is one way to look at the problem: If you do a truth table for ## \neg (A \rightarrow B) ##, you will see that it is logically equivalent to the statement ## A \& \neg B ##. So your first statement is equivalent to ## X \& \neg (Y \rightarrow X) ##. But then that is equivalent to ## X \& Y \& \neg X ##. The basic idea is to use truth table identities to transform the complex statement into simpler ones.
     
  4. Oct 27, 2015 #3
    You can make a truth table with a row for all combinations of y and x. As the columns you use x, y, (y->x), (x->(y->x)) and not(x->(y->x))
    Code (Text):
    x y    (y->x)    x->(y-x)  not(x->(y-x))
    0 0
    0 1
    1 0
    1 1
    If there are only ones in al column, the expression is always true, and if there are only zeros, the expression is never true for any x or y.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook