(Solved): (1) Consider the following transition system TS of the simple beverage vending machine: Figure: A t ...

(1) Consider the following transition system TS of the simple beverage vending machine: Figure: A transition system of the simple beverage vending machine. Prove that $TS???($ soda $?$ beer $),TS??$ soda and $TS???($ soda $?$ beer $)$. 1) For theoretical questions: Your solutions should be clearly presented, for instance, you may need some tools to draw the diagrams, in order to represent your answers clearly. 2) For Promela programming questions, your solutions should have both the source codes of your programs and the screen shots of the running these programs.