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.
Types 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.
The relationship between the four propositions ① the relationship between the 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 and the inverse proposition are reciprocal.
② The relationship between the truth and falsehood of the four propositions: ① The two propositions are mutually negative and have the same truth and falsehood. (2) Two propositions are reciprocal propositions or reciprocal propositions, and their authenticity is irrelevant (whether the original proposition and reciprocal proposition are true or not, whether reciprocal proposition is true or not).