Write the truth table and draw the circuit represented by

$F=(B+D)(A+B^{\text{'}}+C)+(B+D)(C+A)$

$($a$)$ Write the equivalent min term and max term expressions.

$($b$)$ Use K$-$map to find the simplest sum of product expressions. Use K$-$man of the complement to find the simplest of product of sums expression for $F.$

$($c$)$ Write a circuit for $F$ in terms of AND, OR and NOT gates and then convert it to circuit in terms of NAND gates.