In junior high school mathematics, the declarative sentence that can judge whether it is true or false is called a proposition, the correct proposition is called a true proposition, and the wrong proposition is called a false proposition. The following is a summary of relevant contents for your reference.

The definition of proposition in mathematics In mathematics, the declarative sentences that judge things are generally called propositions, and propositions refer to the semantics of judgment (statement) (the concept actually expressed).

This concept is a phenomenon that 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 junior high school mathematics, the declarative sentence of judging something is generally called a 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.

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.

The relationship between truth and falsehood of four propositions:

The two propositions (1) are mutually negative and have the same truth and falsehood. (2) 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).