For each of the descriptions below, write down a table of operation that captures the description. (a) An alarm system is supposed to detect unauthorized entry. There are three inputs, one from the key system (A), and one from each of two doors (B and C). If either door opens (B = 1 or C = 1 or both) when the key system is not activated (A = 0) then the alarm should sound (D = 1). Otherwise, it should not. (b) Modify the table from the previous question so that the alarm also sounds whenever both doors are open, regardless of the state of the key system. (c) An automatic trash compactor can detect when new trash is put into it (A = 1) and also whether it is full (B = 1). The compactor should run (C = 1) whenever new trash is put in, unless it is already full. (d) Whenever the retail stores inventory is low, it sends a request for new product (A = 1) to the distributor. There are two ware- houses, B and C. If warehouse B has the product in stock (B = 1) then it supplies the product (D = 1), otherwise warehouse C supplies the product (E = 1) if it has it in stock (C = 1).