Definition
Truth value
A truth value records the result of checking a statement: true or false.
What it means
The statement is the claim; the truth value is its result after checking. “15 is even” is a statement, and its truth value is false. A different statement can have truth value true.
Remember it
Statement = claim. Truth value = true or false.
Example
For “7 + 5 = 12,” the truth value is true. For “7 + 5 = 13,” the truth value is false.
Watch for
An open sentence such as x + 2 = 9 has no single truth value until x is fixed or the sentence says which values are allowed.
Common mix-up
False statements are still mathematical statements; false is their truth value.
Exact meaning
In classical elementary logic, the truth value of a mathematical statement is one of two values—true or false—once meanings, assumptions, and required variable values are fixed.