* Open sentences express relationships: They describe a relationship between numbers and variables. This relationship is not fixed, it can change depending on the value of the variable(s).
* Variables introduce flexibility: The variables in an open sentence allow for multiple possibilities. The sentence becomes true or false depending on the specific values assigned to the variables.
Example:
* Open sentence: x + 5 = 10
* This sentence is not true or false until we know the value of 'x'.
* If x = 5, the sentence becomes true.
* If x = 2, the sentence becomes false.
Without a variable, the sentence becomes a statement, which is either definitively true or false.
Example:
* Statement: 5 + 5 = 10
* This is always true, regardless of any variables.
Let me know if you'd like more examples!