Proving two boolean expressions

Discussion in 'Homework Help' started by arashb, Oct 5, 2007.

  1. arashb

    Thread Starter New Member

    Oct 5, 2007
    2
    0
    Hi,

    I am trying to prove two boolean expressions by using algebraic simplification.

    I am trying to prove:

    1) ((-a -> -b) /\ (a != b)) \/ ((a /\ c) -> (b /\ c))

    2) (if b then P else if b then Q else R) = (if b then P else R)

    I have proved both using truth tables, but haven't yet using algebra.

    I have tried, but keep going in circles back to the original expression. Any help would be great.

    Thnks
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Firstly, I'm confused by the terminology in your expression; what to the symbols "-", "->", "/\" and "\/" mean?

    Secondly, can you upload your workings so we can have a look? It is easier to guide you on your current attempts rather than teach you a whole something new.

    Dave
     
  3. arashb

    Thread Starter New Member

    Oct 5, 2007
    2
    0
    - means NOT
    -> means implies
    /\ means AND
    \/ means OR


    For the second expression, I have simplified it down to
    (B /\ P) \/ (-B /\ ((B /\ Q) \/ (-B /\ R) ) = (B /\ P) \/ (-B /\ R))

    so I am trying to show that (B /\ Q) \/ (-B /\ R) = R

    The first, I have written it as

    ( (a \/ -b) /\ ((a /\ -b) \/ (-a /\ b))) \/ ((-a /\ c) \/ (b /\ c))
     
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