Please show all work!

1. Which Boolean operation (AND, OR, XOR, or NOT) is appropriate for each of the following: (8 pts) a. Detecting motion in any motion sensor surrounding a house (sensor output is '1' when motion is present) b. Detecting that three buttons are being pressed simultaneously (button output is '1' when pressed) Detecting the absence of light from a light sensor (sensor output is '1' when light is sensed) d. Showing whether a child can have ice cream or candy but not both (having ice cream or candy is shown as a '1') 2. Convert the following English problem statements to Boolean equations. Introduce Boolean variables as needed but make sure to define them first. (9 pts) a. A flood detector will 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