Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Discrete Structures problem

  1. Sep 9, 2008 #1
    OK this is the first assignment I have in this class and I can't figure out how to negate and simplify the logical structure of W <--> S (bi-conditional implication)

    I got this so far:

    ~[(W --> S) ^ (S --> W)] by Definition
    ~(W --> S) v ~(S --> W) by DeMorgan's Law
    ~(~W v S) v ~(~S v W) by Simplification of Implication

    I just don't know where to go to from here. I know the end result would make W <--> S equivalent to W (XOR) S.
  2. jcsd
  3. Sep 9, 2008 #2


    User Avatar
    Science Advisor

    Why the "~"? I would start with (W--> S)^(S-->W).

    Now remember that A-->B is the same as Bv(~A).
  4. Sep 9, 2008 #3
    Well the problem says to find the simplified negation, so I thought that meant to negate then simplify. So I negated the whole thing with ~
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook