Mathematical statement that includes one or more variables and is true for some values attributed to these variables and false in other cases.
The defined set of variables of a propositional form is called the universal set of this propositional form.
- An expression like 3x – 5 = 7 is a propositional form called an equation.
- An expression like 3x – 5 is not a propositional form.
Example
Consider the statement 4x + 1 = 9 This equality, in itself, is neither true nor false. If we define the variable x in the universal set of whole numbers, this propositional form becomes a true proposition when x = 2 and false in all other cases.