$2\mathrm{.}8$ Consider the function $f(a,b,c,d)=a(b^{\text{'}}{c}^{\text{'}}+d).$

a$.$ Find the minterm expansion for $f$ algebraically and write it in $m-$notation.

b$.$ Find the maxterm expansion for $f$ directly from the minterm expansion and write it in $M$ notation.

c$.$ Find the complement of $f$ algebraically. Then find the maxterm expansion for $f^{\text{'}}$ algebraically and write it in $M-$notation.

d$.$ Find the minterm expansion for $f^{\text{'}}$ directly from the maxterm expansion and write it in $m-$notation.