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I'm having some trouble getting a handle with this course. We are starting Boolean algebra and my professor wants us simplify the following:

Im sorry for the ignorance but I can't find a good reference to solve the problem.

  1. $[XY'(Z+YW)+X'Y']Z$
  2. $XY'+ X(Y+Z)'+ Y(Y+Z)'$

I am assuming the "()" with "'" means the over-score above the variables.

joash
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1 Answers1

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Use these rules to solve the questions.

  1. [XY'(Z+YW)+X'Y']Z => [XY'Z + XY'YW + X'Y']Z (Distributive Law)=> [XY'Z+X'Y']Z (Complementary Law) => XY'Z+X'Y'Z => Y'Z(X+X') (Distributive Law) => Y'Z (Complementary Law followed by Law of Intersection)

  2. XY'+ X(Y+Z)'+ Y(Y+Z)'=> XY' + XY'Z' + Y(Y'Z') (De Morgan's Law and Distributive Law)=> XY'(1+Z) (Distributive Law and Complementary Law) => XY' (Law of Union followed by Law of Intersection)

Ashish Gupta
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  • Hi Ashish Gupta, – joash Oct 11 '15 at 06:31
  • @joash Hi. Did you understand what I did? – Ashish Gupta Oct 11 '15 at 06:34
  • Hi Ashish Gupta, Just have some question on your answers.... on the 1st question could you elaborate how XY'YW been gone in the expression and result on [XY'Z+X'Y']Z..... and on the second question why does X(Y+Z)' became xy+xz isn't suppose to be xy'z' – joash Oct 11 '15 at 06:56
  • Corrected the mistake in the second question. As for the first question, XY'YW can be written as X(Y'Y)W. Y'Y = 0 as per the Complementary law, and anything multiplied by 0 is 0 as per the Law of Intersection. As for [XY'Z+X'Y']Z, I just opened the bracket. XY'ZZ is same as XY'Z because ZZ = Z as per Idempotent Law. – Ashish Gupta Oct 11 '15 at 07:01
  • thnks men for the big help... – joash Oct 11 '15 at 07:19
  • hi Ashish Gupta, 1 more question can you check out this equation.. X’YZ + XY’Z’ + X’Y’Z’ + XY’Z + XYZ my answer is x'yz+y'z'+xz but badly not sure of it! – joash Oct 11 '15 at 07:52
  • hi Ashis Gupta , can you check this equation X’YZ + XY’Z’ + X’Y’Z’ + XY’Z + XYZ my answer is x'yz+y'z'+xz but badly not sure of it! can you check thnks in advance – joash Oct 11 '15 at 08:07