Discrete Structure (1) - proposition and consistent system

Why proposition?

In the real world, we use English or any other language to explain the logical structure. For example, In this September, US Open tennis was held in New york city. Or, 4 is not the prime number. It's the best and easiest way to explain the sentence to people. But sentences could be ambiguous. So we use propositional logic. Direct and simple. That is the key point. 

 

Proposition

p → q (p implies q)

There are many ways of saying this proposition. 

• If p, then q
• p is sufficient for q
• q if p
• q when p...

Here is some example.

• Roads will be wet(p), if it rains(q) = q → p
• I will go to the class(p) if I want to(q) = q → p

 

That's why we use proposition. Simple is best + Easy to understand

 

We know the Logical operator and Proposition. After this, we have to learn about Consistent System. I can say the purpose of the logical operator and proposition is for Consistent System.

 

 

Consistent System

A propositional system is consistent if there exist a set of values for each proposition, such that the entire is consistent. It means given propositions have to be ALL TRUE. Then we call it consistent.

 

Example

Consistent System

 

Isn't it simple? 

If you have some time try the truth-teller quiz. It is also a consistent system based quiz.