$($Total: $20$ points$)$ Draw the logic diagram corresponding to the following Boolean expression:

a$)$ points$)F_1=A^{\text{'}}{B}^{\text{'}}+Ao+B+(A+C{)}^{\text{'}}$

b$)(10$ points$)$ Write a Boolean expression for the following logic Diagram. To get full points, you must write the final answer in a standard format.

Note: You must show the detail of your work to get full points.