My Math Forum Boolean Algebra -simplify and basic stuff

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 September 18th, 2014, 12:53 AM #1 Newbie   Joined: Sep 2014 From: Sweden Posts: 1 Thanks: 0 Boolean Algebra -simplify and basic stuff Hi! I have a course in Digital Design and honestly, i find it super difficult, so instead of getting nowhere i decided make a thread and ask some questions . Can i simplify this boolean equation any further: f(x,y,z) = z(x'+y) + xy'z = z(x'+y+xy') Thanks in advance
 September 18th, 2014, 03:49 AM #2 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 You can verify that $x'+y+xy'=1$ using a truth table. Symbolically, \begin{align} x'+y+xy'&=x'(y+y')+y+xy'\\ &=x'y+x'y'+y+xy'\\ &=x'y'+y+xy'&&\text{since }x'y+y=(x'+1)y=1y=y\\ &=y'(x+x')+y\\ &=y'+y\\ &=1 \end{align} Thanks from Deveno
September 18th, 2014, 05:56 AM   #3
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Quote:
 Originally Posted by Evgeny.Makarov You can verify that $x'+y+xy'=1$ using a truth table.
Indeed. Argument with words: if x is false you're done, otherwise x is true and you have y + y' which is always true.

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