Answer to Question #140222 in Discrete Mathematics for sai

Question

Use Karnaugh map to minimize the sum of product expansion
xy'z+ xy'z'+x'yz+x'y'z+x'y'z'

Answer 1

$\text{create a Karnaugh map}$

$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \frac{yz}{x} & 00 &01&11&10 \\ \hline 0 & 1 & 1&1&0 \\ \hdashline 1 & 1& 1&0&0 \end{array}$

$\text{Let's select on the Karnaugh map rectangular areas of units of the largest area,}$

$\text{which are powers of two, and write out the conjunctions corresponding to them:}$

$\text{region 1}$

$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \frac{yz}{x} & 00 &01&11&10 \\ \hline 0 & \color{red}1 &\color{red} 1&1&0 \\ \hdashline 1 & \color{red}1& \color{red}1&0&0 \end{array}$

$K_1:y'$

$\text{region 2}$

$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \frac{yz}{x} & 00 &01&11&10 \\ \hline 0 & 1 & \color{red}1&\color{red}1&0 \\ \hdashline 1 & 1& 1&0&0 \end{array}$

$K_2:x^{\prime}z$

$\text{Combining them using the OR operation, we get}$

$y'+x'z$

Answer: $y'+x'z$