What Is an Open Sentence?


Quick Answer

In mathematics, an open sentence is an algebraic expression without a definite truth value, which means that the statement's veracity or falsity is uncertain. Open sentences contain variables, which are denoted by letters to represent unknown values.

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Full Answer

Mathematical sentences can either be closed or open. A closed sentence is an expression whose truth value is known, either the sentence is always true or always false. An example of a closed sentence is, "The number 2 is the smallest prime number." This statement is always true under any condition.

An open sentence, meanwhile, can either be true or false depending on what value is supplied for the variable. For instance, the expression "X is a whole number" is only true if the value of the variable "X" is any positive integer or 0. Otherwise, the sentence is false.

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