Consider the following K map, on variables A$,$ B$,$ C$,$ and D$.$ CD $00011110$ AB $001100010111110111101100($a$)(2$ marks$)$ List all prime implicants, and indicate which ones are essential prime implicants. $($b$)(2$ marks$)$ Using only prime implicants, find at least two different ways of writing the function in fully reduced sum$-$of$-$products form. $($c$)(1$ mark$)$ In the fully reduced sum$-$of$-$products expression, why are there no implicants other than prime implicants?