Results 1 to 9 of 9
Like Tree6Thanks
  • 1 Post By chiro
  • 2 Post By chiro
  • 2 Post By chiro
  • 1 Post By chiro

Math Help - Simple Proof table problem

  1. #1
    Newbie
    Joined
    Sep 2013
    From
    Canada
    Posts
    5

    Simple Proof table problem

    For some reason I can't wrap my head around this one...

    I am supposed to use truth tables to explain expressions like

    x 1 = x
    x ⊕ 1 = xnot
    x ⊕ 0 = x
    etc, etc.

    Obviously I can do something like

    x
    x ⊕ 1
    0
    1
    1
    0

    but that seems redundant and doesn't really explain how I came to that conclusion. Is there anyway I can expand this truth table to make it clear how I came my conclusion? Any help would be appreciated, thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Simple Proof table problem

    Hey HelpMeWanda.

    What does the ⊕ mean? Usually in binary mathematics its an XOR operator - is this the case here?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2013
    From
    Canada
    Posts
    5

    Re: Simple Proof table problem

    That's right, it's XOR, sorry for not being clearer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Simple Proof table problem

    The first expression is wrong but the other two are ok. Basically you should just construct a truth table which will have four possibilities and calculate c = a AND not(b) d = b AND not(a) and e = c OR d.
    Thanks from topsquark and HelpMeWanda
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2013
    From
    Canada
    Posts
    5

    Re: Simple Proof table problem

    Ok, I see what you're saying and I've been trying to do that, but I have trouble making the conclusion work. The problem is that whenever I add a second variable to the truth table, it makes it so x(not) has a TRUE value in a row that isn't XOR. I'm having trouble explaining this I think, so I will draw out my truth table and show what's wrong.


    x y x(not) y(not) x(not) AND y x AND y(not) x(not) AND y OR x AND y(not)
    0 0 1 1 0 0 0
    0 1 1 0 0 1 1
    1 0 0 1 1 0 1
    1 1 0 0 0 0 0

    So going by this table, it would seem x⊕y doesn't equal x(not) like it is supposed to. The only way it works is if I use one variable, the problem being I don't know how to flesh out a 1 variable truth table that explains how I came to this conclusion.
    Last edited by HelpMeWanda; September 28th 2013 at 07:03 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Simple Proof table problem

    You have to remember that y is fixed in your questions. In the order of the questions given, you have y = 1, 1, 0. Substitute these in and see if you get a contradiction or not (you should get a contradiction for the first statement).
    Thanks from topsquark and HelpMeWanda
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2013
    From
    Canada
    Posts
    5

    Re: Simple Proof table problem

    Wow thank you so much, I think I get it now.

    Just to make sure though, given the way these questions were asked, is this acceptable:

    x y
    0 1
    0 1
    1 1
    1 1

    Sorry I think that's wrong... for some reason like I said I just can't wrap my head around this... I really appreciate your help and patience though.
    Last edited by HelpMeWanda; September 28th 2013 at 08:58 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Simple Proof table problem

    You can remove the duplicates which will give you two rows.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Sep 2013
    From
    Canada
    Posts
    5

    Re: Simple Proof table problem

    Thank you so much! You're a life saver.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple truth table, check if correct
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 18th 2013, 08:04 AM
  2. Simple logic truth table question
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: April 13th 2013, 10:00 AM
  3. Replies: 2
    Last Post: January 23rd 2013, 03:19 AM
  4. (Simple?) combination problem (proof required)
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: August 31st 2009, 08:44 AM
  5. Proof with Simple Problem
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: January 17th 2008, 08:09 PM

Search Tags


/mathhelpforum @mathhelpforum