Show that expressions are equivalent

Discussion in 'Homework Help' started by Bangersandmash, Sep 27, 2016.

  1. Bangersandmash

    Thread Starter New Member

    Jun 10, 2016
    26
    0
    Hi Would anybody be able to check to see if my workings are right for this question?

    Thanks
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,143
    1,790
    It appears that the final column is wrong in the first table. You need to state your conclusion based on the truth tables.
     
  3. Bangersandmash

    Thread Starter New Member

    Jun 10, 2016
    26
    0
    Hi Papa

    Should the last column from each table have the same values to prove they are equivalent?
     
  4. AlbertHall

    Well-Known Member

    Jun 4, 2014
    1,941
    383
    The expression in the final column of the first table is not the same as the left hand expression in the question - you are missing some 'not's.
     
  5. Papabravo

    Expert

    Feb 24, 2006
    10,143
    1,790
    Yes, the columns on the right hand side of both tables should be the same. If they are the same, then you should also be able to prove algebraically that the expressions are the same.
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,743
    4,795
    You have actually made several mistakes.

    First, your first truth table is for an expression different from the left hand side of what you are trying to prove, so therefore it is not convincing.

    Second, you have tried to apply DeMorgan's to get from the original left hand side to what you have in the first truth table and you made two mistakes. First, you kept the operation between terms as an OR instead of changing it to an AND. Second, you made the common mistake of replacing (B·C')' with (B'·C). Doesn't work that way. Although both of your mistakes are consistent, leading me to question whether you understand DeMorgan's Theorems at all. Go back and review them.
     
  7. RBR1317

    Active Member

    Nov 13, 2010
    232
    48
    Just a few applications of DeMorgan's Theorem would show the equivalence via Boolean algebra:
    Screenshot from 2016-09-27 18-00-32.png
     
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