Definition and types of propositions

In mathematics, a statement that judges something is generally called a proposition. Next, we share the definition and classification of propositions.

Definition of Proposition

In modern philosophy, mathematics, logic, and linguistics, a proposition is the semantics (the concept actually expressed) of a judgment (statement) that is a phenomenon that can be defined and observed. A proposition does not refer to the judgment (statement) itself, but to the semantics expressed. When dissimilar judgments (statements) have the same semantics, they express the same proposition. In mathematics, a statement that judges something is generally called a proposition.

Types of propositions

① Original proposition: a proposition by itself is called an original proposition, e.g., if x>1, then f(x)=(x-1)^2 is monotonically increasing.

② Inverse proposition: a new proposition that reverses the conditions and conclusion of the original proposition, e.g., if f(x) = (x-1)^2 monotonically increasing, then x>1.

③ Negative proposition: a new proposition that negates all of the conditions and conclusions of the original proposition but does not change the order of the conditions and conclusions, e.g., if x<=1, then f(x) = (x-1)^2 not monotonically increasing.

④ Inverse Negative Proposition: a new proposition that reverses the conditions and conclusion of the original proposition, and then negates the conditions and conclusion in their entirety, e.g., if f(x) = (x-1)^2 is not monotonically increasing, then x<=1.