What is mathematical proposition?

What Does mathematical proposition Mean

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

The mathematics , on the other hand, is the science devoted to the analysis of abstract entities such as numbers, shapes 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 an algebraic expression that can carry two values : be true or be false , although never both at the same time.

Denominated through lowercase letters, mathematical propositions have a truth value (which will be the truth or falsity of their statement). According to their characteristics, it is possible to distinguish between simple propositions (which lack logical connectors ) and compound propositions (they have more than one logical connector). Within these groups can also noted other classifications: relational propositions , predicative propositions , etc.
Mathematical propositions can be seen as expressions of judgment that cannot be both 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 is 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 between the multiples of 3 ( 3 x 2 = 6 , 3 x 3 = 9 ).
Open mathematical proposition
There are certain statements of which we cannot anticipate their truth value with the naked eye, since in their content there is at least one variable , the value of which 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 whether the proposition is true or false.
In some cases, variables can be replaced by more than one value, which are part of a set called the domain of the variable . In turn, the set that is formed by the elements of said domain that make the open proposition true is called the solution set of the open proposition .

Conjunctive mathematical proposition
When two propositions are joined through the conjunction symbol (^), we speak of a conjunctive proposition, which must meet the following condition : it can only have a true truth value if its two components are also true; On the other hand, if at least one of them returns false , then the conjunctive sentence 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 intersection set of both mathematical propositions.
Disjunctive mathematical proposition
In this case, two propositions are also connected, but the opposite symbol to the previous one is used, which can be read as the word "or", since it proposes a relationship characterized by the following requirement: the disjunctive proposition can only have a true value if its two components turn out to be false, while it is enough that one of them is true so that the first one is also true.
Implication
Este tipo de proposición matemática también se denomina condicional y consiste en una conexión que tiene lugar si se cumple lo siguiente: es falsa sólo cuando la primera proposición (denominada antecedente) es verdadera y la segunda (el consecuente) es falsa; cualquier otro caso dará como resultado un valor verdadero.

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