I'm given this expression
$$
(x+y'+z')(x'+z')
$$
the $'$ meaning not. I have to simplify this to 3 literals and show my answer as a product of sums.
Every calculator I check says the answer is $(x'y')+z'$. So far all I can think of to do as the first step is to expand the given expression using distribution giving me
$$
xx'+xz'+x'y'+y'z'+x'z'+z'z'.
$$
From there I know $xx'$ is $1$ and $z'z'$ is $z'$, giving me $xz'+x'y'+y'z'+x'z'+z'$ and this is where I get stuck. Any suggestions?
Best Answer
Expression $xx'$ means “$x$ is true and not $x$ is true”, so $xx'=0$. Thus the expression is: $$ xz'+x'y'+y'z'+x'z'+z'z'=(x+x')z'+x'y'+y'z'+z'= x'y' + (y'+1)z'=x'y'+z' $$