Definitions, axioms, formulas, properties, laws and theorems in mathematics are all mathematical propositions. These are the basis for judging whether the proposition is true or false through reasoning.
Generally speaking, in mathematics, we call statements that can be expressed in language, symbols or formulas within a certain range and can judge whether they are true or false as propositions. Mathematical proposition usually consists of two parts: the topic is known matter, and the conclusion is matter derived from known matter.
The relationship between propositions:
1, the relationship between four propositions: the original proposition and the inverse proposition are reciprocal, the negative proposition and the original proposition are reciprocal, the original proposition and the inverse proposition are reciprocal, and the inverse proposition is reciprocal.
2. The relationship between the truth and falsehood of the four propositions: the two propositions are mutually negative and have the same truth and falsehood. Two propositions are reciprocal propositions or reciprocal propositions, and their truth values are irrelevant (the original proposition and reciprocal proposition are true and false, and reciprocal proposition is true and false).
3. A declarative sentence that can judge whether it is true or false is called a proposition, a correct proposition is called a true proposition, and a wrong proposition is called a false proposition.