Gloria's Jeans wants to hire you to design their automated coffee machine. They want their machine to be able to make three of their most popular coffee flavors: 'Shot of espresso', "Latte" and "Mocha". Basic ingredient for any of these flavors are Brewed Coffee, ful cream milk, sugar and coco powder. Input and output of the automated coffee machine is as follows: Input (4 variables C = 1 indicates presence of Brewed coffee. M= 1 indicates presence of full cream milk S = 1 indicates presence of sugar. K = 1 indicates presence of Cocoa Powder Output (3 variable) E = 1 indicates Shot of Espresso is ready L = 1 indicates Latte is ready M = 1 indicates Mocha is ready. Gloria's Jeans authorities has asked you to consider the following points when designing the system: 1. Without brewed coffee it is impossible to make any type of coffee. 2. Brewed coffee and milk are essential for making Latte. Sugar is n optional(may or may not be there) ingredient. You do not need cocoa powder to make Latte. 3. Brewed coffee, cocoa powder and milk are essential for making 'Mocha'. Sugar (may or may not be there) is an optional ingredient. 4. 'Shot of Espresso' is just brewed coffee. Sugar is an optional ingredient. Cocoa powder and milk is not at all needed to make 'Shot of Espresso'. a) Using the above specification, prepare a truth table for the automated coffee machine. b) Using 4 variable Karnaugh-Map method, derive SOP expressions for all of the three flavors of coffee mentioned above