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Boolean Algebra Proof

  1. Jul 22, 2004 #1
    I think I am missing part of my notes, or at least I don't understand them:

    if x+y = y+z and xy = xz, then x=z

    x = (y+z)x Absorbtion (Don't really know where this is coming from)
    x(y+z) Commutative
    xy+xz Distributive
    It stops here and starts again at:

    yz+xz (I have no idea where this came from)
    zy+zx Commutative
    z(y+z) Distributive
    (z+y)z Here is where it gets confusing. Where did the z+y come from?
    z Proven previously
     
  2. jcsd
  3. Jul 23, 2004 #2
    I think the easiest way of showing that is by using truth tables.

    x + y = y + z --> x(x + y) = x(y + z). Note that the left hand side simplifies to x, hence the result above.

    x + y = y + z --> (x + y)z = (y + z)z. The left hand side equals what you have above. Note that the right hand side simplifies to z.

    Just rearrange the terms from the previous step, i.e. z(y + z) = (z + y)z.

    It's not clear to me what is going on here. Are these the steps from an exercise in a book?

    [edit]I just noticed that these are supposedly notes. I've never taken any notes in any maths. class (or most classes for that matter). I think it would do you wonders to understand what's happening here rather than deciphering what notes you're missing.[/edit]
     
    Last edited: Jul 23, 2004
  4. Jul 23, 2004 #3
    It was an example the teacher did on the board, but I couldn't copy it down fast enough before it was time to go, so some of the lines I just scribbled and I am pretty sure some of the stuff is missing.
     
  5. Aug 21, 2004 #4
    The solution for this problem


    Here the first statement (x=z)it self is the place you all have missed. And it has the soution. Hence you might be starting this formular from the middle.
    Becuse of that x=(y+z)x is your starting point.

    xy+xz becomes yz+xz because (x=z;first statement) so you have put z instead of x for xy and you haven't chaned xz which is perfectly correct.

    And zy+zx becomes (z+y)z because you can write zy+zx as (y+x)z and it can be writen as (z+y)z just by replacing x with z (x=z;first statement)

    If you have a doubt about this or if you have any problem regarding maths please mail me through the following e mail supundikadl@yahoo.co.uk
     
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