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

$f(x,y,x)=x^{\text{'}}y+y^{\text{'}}{z}^{\text{'}}+xyz$

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

b$)(1$ point$)$ List all the minterms of function $f$ in $$ notation.

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

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

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