DIGTIAL LOGICAL DESIGN EXPERTS PLEASE SOLVE

Q$1(10$ points$)$ Given the following Boolean function:

a$)(4$ points$)$ Fill the truth table of the function $f.$

$\backslash$table$[[xyz,x^{\text{'}}y,y^{\text{'}z},xyz,$f$],[000,,,,],[001,,,,],[010,,,,],[011,,,,],[100,,,,],[101,,,,],[110,,,,],[111,,,,]]$

b$)(1$ point$)$ List all the minterms of function $f$ in ${\displaystyle \underset{?}{\overset{?}{}}}$ notation.

c$)(2$ points$)$ Write the sum$-$of$-$minterms $($SOM$)$ expression for $f.$

d$)(1$ point$)$ List all the maxterms of function $f$ in prod notation.

e$)(2$ points$)$ Write the product$-$of$-$maxterms $($POM$)$ expression for $f.$