Simplify the following Boolean function using a K$-$map. You must show the K$-$map and

indicate your groupings to show how you arrived at the simplified function.

$F(a,b,c,d)=a^{\text{'}}{b}^{\text{'}}cd+a^{\text{'}}b{d}^{\text{'}}+a{b}^{\text{'}}d+ab$

Draw the circuit for the simplified function in problem above

What is the complement of the simplified function in problem above

Redraw the circuit for the simplified function in problem above using only NAND gates.

Redraw the circuit for the simplified function in problem $3$ using only NOR gates.