Trying to understand SATISFIABILITY

Question

I am not a mathematics student but am trying to understand SATISFIABILITY as part of a project i am working on.

As i Understand it, basic SAT has the equation; x or not x. True or False, Yes or No.

The project i am working on is one where at each occurance of the question the event occurance asks 3 seperate SAT questions.

The basics are thus. i have an ongoing infinate random selection process. each event that occurs during this process is defined by 3 different combined choices.

for example. ( ' = not)

the next event will be ((x or 'x) and (y or 'y) and (z or 'z))

To put this into a real world scenario the following stands as an example

There are 3 boxes which contain a black and white ball in each (6 balls total)
Without looking a ball is chosen from each box giving a 3 ball combination which represents the full event occurance. Balls are then returned to the box and the selection process then begins again.

Another example would be the tossing of 3 coins at one time and looking at the 3 different results as ONE event occurance So the possible outcomes to the event occurance are,

(x and y and z) 3 heads/black balls
(x and y and 'z) 2 heads/blacks 1 tails/white

(x and 'y and z) 2 heads/blacks 1 tails/white

(x and 'y and 'z) 2 tails/whites 1 heads/black

('x and y and z) 2 heads/blacks 1 tails/white

('x and 'y and z) 2 tails/whites 1 heads/black

('x and y and 'z) 2 tails/whites 1 heads/black

('x and 'y and 'z) 3 tails/white balls

Before each event occurance the observer is tasked to predict which of the outcomes will occur by stating one of the above 8 possibilities.. After the event has occured the result is compared to the prediction to see if if the result matches.

 

e.g. A prediction is made; xy'z. the result is xyz. the predictions for x and y are satisfied but z is not.

Is this a 3-SAT problem?

 

If not, can somebody define the above problem in terms of Satisfiability. Any help would be much appreciated.

Answer 1

     There is a simple principle in mathematics that I think better illustrates your needs. It is called the trichotomy principle for Real numbers. It goes like this.

If x and y a Real numbers, then either x<y, x=y, or x>y. 

If you pick any two Real numbers, one of these must be true.

 

So, you input a pair of numbers and the decision box will lead you along to one of three paths. This is an expansion of the typical computer decision box which sends you in a particular direction based on your answer to one question. It's like a line on an application  or a tax return that says if you're single and make more than 20000, skip to line 10. if you're single and make between 20000 and 100000, skip to line 20 but if you are single and make more than 100000, skip to line 30. For each single person that reads this, they fall into one category and are then directed to the appropriate next question based on that single answer.

 

I hope you find this helpful.