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Mathematical Proposition


Proposition It is a concept with different uses. It may be the manifestation of something so that other individuals know an intention, the concretion of a proposal or a statement that may be false or true.

The math On the other hand, it is science dedicated to the analysis of abstract entities, such as numbers, geometric figures and symbols, and their properties. As an adjective, the term refers to everything related to this deductive discipline.

After these clarifications, we can focus on the mathematical propositions . A mathematical proposition is a algebraic expression which can carry two values : be true or be false , although never both at once.

Named through lowercase letters, mathematical propositions have a real value (which will be the truth or falsity of your statement). According to its characteristics, it is possible to distinguish between simple propositions (lacking connectors logical ) and compound propositions (They have more than one logical connector). Other classifications can also be seen within these groups: relational propositions , predicative propositions , etc.

Mathematical propositions can be seen as expressions of judgment that cannot be true and false simultaneously. For example:

a: 9 is a multiple of 3

This expression is a mathematical proposition that is true, since 3 x 3 is equal to 9 and therefore, 9 It's one of the infinite multiples of 3 . As we said above, the mathematical proposition can also be false:

b: 7 is a multiple of 3

In this case, the proposition is false since 7 is not among the multiples of 3 (3 x 2 = 6 , 3 x 3 = 9 ).

Open mathematical proposition

There are certain statements of which we cannot anticipate its value of truth at first sight, since in its content there is at least one variable , whose value is unknown. After observing and analyzing it, the necessary calculations can be carried out to find one of the values ​​capable of replacing it, to finally be in a position to ensure that the proposition is true or false.

In some cases, the variables can be replaced by more than one value, which are part of a set called variable domain . In turn, the set that is formed by the elements of said domain that return the true open proposition is called set open proposition solution .

Conjunctive mathematical proposition

When two propositions are joined through the conjunction symbol (^), we speak of a conjunctive proposition, which must comply with the following condition : can only have a real value true if its two components are too; instead, if at least one of them throws the value false, so the conjunctive proposition is false.

Since it is the relationship between two sets, it is also possible to determine those elements that are part of both domains of variables, which belong to the set intersection of both mathematical propositions.

Disjunctive mathematical proposition

In this case, two propositions are also connected, but the symbol opposite to the previous one, which can be read as the word "o", since it proposes a relationship characterized by the following requirement: the disjunctive proposition can only have a true value if its two components are false, while one of them is enough be true so that the first one is also true.


This type of mathematical proposition is also called conditional and consists of a Connection which takes place if the following is true: it is false only when the first proposition (called antecedent) is true and the second (the consequent) it is false; any other case will result in true value.