Using Logic gate Tom's Cafeteria orders a machine to dispense Coffee$($c$),$ Tea$($t$),$ and Milk$($m$).$ The machine has a button$($ input line $)$ for each choice. However $,$ a customer can have at most, just one of the three choices. The input and output variable and $($and their states$)$ are as follows :

Input $,$ c $=$ coffee button $(1=$ pushed $,0=$ not pushed$),$ t $=$ tea button $(1=$pushed, $0=$ not pushed$),$ m $=$ milk button $(1=$ pushed $,0=$ not pushed$)$ 

a$.$ Write a Boolean expression to represent an acceptable input $($i$.$e$.$ x$=1).$

b$.$ Using only AND, OR and NOT gates, draw a logic circuit for this system.

c$.$ Construct a truth table to represent the logic of this machine.