Problem $4$: $(25$ points$)$

a$.$ Let $f(x,y,z)=x^{\text{'}}y+y^{\text{'}}{z}^{\text{'}}+yz+xz$ be a Boolean function. Give the truth table of $f,$ and put $f$

in DNF and CNF$.$

b$.$ Minimize each of the following Boolean expressions using Karnaugh maps.

i$.,x^{\text{'}}{y}^{\text{'}}+yz+y^{\text{'}}{z}^{\text{'}}+xz$

ii$.,yz+x^{\text{'}}{z}^{\text{'}}+x{y}^{\text{'}}z+x^{\text{'}}z$

iii. $,x^{\text{'}}y{w}^{\text{'}}+x{y}^{\text{'}}w+x^{\text{'}}{z}^{\text{'}}{w}^{\text{'}}+x^{\text{'}}{y}^{\text{'}}z{w}^{\text{'}}$

iv$.,x^{\text{'}}yz+x{y}^{\text{'}}{y}^{\text{'}}{w}^{\text{'}}+y{z}^{\text{'}}{w}^{\text{'}}+x{y}^{\text{'}}{z}^{\text{'}}{w}^{\text{'}}+y^{\text{'}}zw+xyzw$