$(10$ marks$)$ Consider the boolean function $f(x,y,z)=\frac{x\frac{+}{b}ar(y)}{b}ar((xy+z))+x(\frac{?}{\text{b}\text{a}\text{r}}(y)+yz).$

$($a$)$ Find the values of the Boolean function represented by $f(x,y,z)=\frac{x\frac{+}{b}ar(y)}{b}ar((xy+z))+x(\frac{?}{\text{b}\text{a}\text{r}}(y)+yz),$ and display these values in a table.

$($b$)$ State both the conjunctive and disjunctive normal forms of $f.$

$($c$)$ From the disjunctive normal form, obtain a minimal sum$-$of$-$products expression for $f$ using either a Karnaugh map or the Quine$-$McCluskey method.