A sentential formula that contains at least one free variable. A sentential variable containing no free variables (i.e., all variables are bound) is called a closed sentential formula. Examples of open sentential formulas include exists y(x = 2y), which means that x is even (over the domain of integers), and x>1⋀ for all u for all v(x!=(u + 2)(v + 2)), which means that x>1 and x is not the product of two numbers (both greater than one), i.e., x is prime. Closed sentential formulas are known as sentences, although it sometimes also happens that open sentential formulas are admitted as sentences.
