A museum has three rooms, each with a motion sensor (m2, m1, m0) that outputs 1 when motion is detected. At night, the only person in the museum is one security guard who walks from room to room. Design a device that receives a 3-bit binary number (m2, m1, m0) and sounds an alarm (by setting an output f to 1) whenever motion is detected in more than one room at a time (meaning there must be an intruder or intruders in the museum). a. Show the truth table of the device. b. Write sum-of-minterms and product-of-maxterms expressions for f