$(10$ pts$)$ Find the minimum sum$-$of$-$products $($SOP$)$ and product of sums $($POS$)$ expression for the following Boolean function. Specify the essential prime implicants and tell $($circle$)$ which minterm makes each one essential. $(6$ Points$)[$an extra map is provided for scratch work if you need it$]$

$f(A,B,C,D)=M(0,1,2,3,15)D(5,6,7,8,9,10)$

$\backslash$table$[[CD,00,01,11,10],[00,,,,],[01,,,,],[11,,,,],[10,,,,]]$

SOP:

$F(A,B,C,D)=$

POS:

$F(A,B,C,D)=$