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September 18th, 2014, 12:53 AM   #1
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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
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September 18th, 2014, 03:49 AM   #2
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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}
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September 18th, 2014, 05:56 AM   #3
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Quote:
Originally Posted by Evgeny.Makarov View Post
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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