Convert the following English problem statements to Boolean equations. Introduce Boolean variables as needed.

a$)$ A flood detector should turn on a pump if water is detected and the system is set to enabled.

b$)$ A house energy monitor should sound an alarm if it is night and light is detected inside a room, but motion is not detected.

c$)$ An irrigation system should open the sprinkler's water valve if the system is enabled and neither rain nor freezing temperatures are detected.

Convert the following Boolean equations to a digital circuit schematic:

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

b$)F(a,b,c)=abc+ab+a+b+c$