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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


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    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 ~
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