Definition of Proposition In modern philosophy, mathematics, logic and linguistics, a proposition refers to the semantics of a judgment (statement) (the concept of actual expression), which can be defined and observed. Proposition refers not to the judgment (statement) itself, but to the semantics expressed. When different judgments (statements) have the same semantics, they express the same proposition. In mathematics, a declarative sentence to judge something is generally called a proposition.
The form of the proposition 1 For two propositions, if the conditions and conclusions of one proposition are the conclusions and conditions of another proposition, then these two propositions are called reciprocal propositions, one of which is called the original proposition and the other is called the inverse proposition of the original proposition.
2. For two propositions, if the conditions and conclusions of one proposition are the negation of the conditions and conclusions of the other, then these two propositions are called mutually negative propositions, one of which is called the original proposition and the other is called the negative proposition of the original proposition.
3. For two propositions, if the condition and conclusion of one proposition are the negation of the conclusion and condition of the other proposition, then these two propositions are called mutually negative propositions, one of which is called the original proposition and the other is called the negative proposition of the original proposition.
Classification of propositions ① Original proposition: A proposition itself is called the original proposition. For example, if x> 1, then f (x) = (x- 1) 2 monotonically increases.
② Inverse proposition: a new proposition with the opposite conditions and conclusions to the original proposition, such as f (x) = (x- 1) 2 monotonically increasing, then x> 1.
③ No proposition: a new proposition that completely negates the conditions and conclusions of the original proposition, but does not change the order of conditions and conclusions, for example, if X.
④ Negative proposition: a new proposition that reverses the conditions and conclusions of the original proposition and then completely negates it, such as: if f (x) = (x- 1) 2 does not increase monotonically, then x < = 1.