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Boolean Algebra Simplification Property Question

  1. Jun 18, 2013 #1
    Hi I am not sure where to post this question but I am trying to simplify this expression:

    r*c'w+c (As in R AND NOT C AND W OR C) to c+wr (As in C OR W AND R) and I know that it simplifies to this and they are both equivalent; however my question is which boolean simplification property is used here? Is it the Absorption principle? Thank you!
     
  2. jcsd
  3. Jun 18, 2013 #2
    No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

    Is this homework?
     
  4. Jun 18, 2013 #3
    No it's a worked example left for us to solve if we wanted extra practice. And that's what I thought initially. So it is using the distributive property and then the complement theory. Thank you.
     
  5. Jun 18, 2013 #4
    Also one last question. When expressions are functionally equivalent like the two above, can they always be reduced to being identical? I am assuming yes, because they are equal to begin with, correct?
     
  6. Jun 18, 2013 #5
    Two Boolean expressions that have the same variables are equal if and only if they have identical truth tables.
     
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