The Boolean function $F(x,y,z)={\displaystyle \underset{?}{\overset{?}{}}}m(0,3,7)$ represents a sum minterms, which of the following represents the canonical form of $F(x,y,z)?$

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

B$)F(x,y,z)=x+y+z$

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

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

E$)$ none of the above.

$29.$

The Inverse $F^{\text{'}}$ of the Boolean function $F(x,y,z)=$prodM$(0,3,6)$ can be stated as

A$)F^{\text{'}}={\displaystyle \underset{?}{\overset{?}{}}}m(1,2,4,5,7)$

B$)F^{\text{'}}=(x+y^{\text{'}}+z)(x^{\text{'}}+y+z^{\text{'}})(x^{\text{'}}+y^{\text{'}}+z)$

C$)F^{\text{'}}=x*y+x*z^{\text{'}}+y*z$

D$)F^{\text{'}}=x*z^{\text{'}}+y^{\text{'}}+x*y$

E$)$ none of the above.

$30.$

Which Boolean function is implemented by this circuit $($Hint: $a$CORb$=a{b}^{\text{'}}+a^{\text{'}}b)$

A$)f=y$ and $g=x^{\text{'}}{y}^{\text{'}}$

B$)f=x^{\text{'}}$ and $g=(x+y{)}^{\text{'}}$

C$)f=x^{\text{'}}+y$ and $g=x^{\text{'}}{y}^{\text{'}}$

D$)f=g$

E$)$ none of the above.