For propositional logic, it is generally only necessary to define five commonly used conjunctions (from a mathematical point of view, each conjunction is a function, and the independent variable of each proposition is a variable, and the result is determined by the relationship between the independent variable and the function).

Namely disjunction, conjunction, conditional implication, negation and equivalence.

In fact, propositional logic only needs to define a conjunction; All formal formulas of propositional logic can be expressed by only one conjunction and propositional argument, whether it is binary propositional logic or multivariate propositional logic.

The proof process is a bit long, so here are some key points: (I don't like the complexity of mathematical language, so I usually use graphic methods to be intuitive and easy to understand, and the logic is not inferior to mathematical language, but I don't draw because I type on my mobile phone)

1. This graph consists of propositional functions of two propositional arguments, * * *16; The truth tables of these 16 functions form a truth matrix diagram;

Secondly, according to this diagram, we can easily find out the transformation relationship of this 16 function, that is, we can get the equivalent formula of the propositional formula.

At present, there is only one problem about propositional logic that has not been completely solved. It can be said that I am proficient in propositional logic.