Given that $Ao.B$ has the truth table in Figure $1$:

a$.$ Write the equivalent expression of $Ao.B$ using only NOT, AND, and OR gates $($no parenthesis$).(10$ points$)$

b$.$ Use DeMorgan's Theorem on the expression from part a to find the equivalent of $(Ao.B)\text{'}$ using only NOT, AND, and OR gates $($no parenthesis$).$