We want to add a constant to language that denotes or .
How to Show a System is NOT Adequate
Suppose we want to show is not adequate. We must construct a truth table of some formula that has some property that can’t be a property of a truth table of any formula created in the system . For this example, we have that no formula in this system can evaluate to true given that all the variables are have value (this is a property that needs the operator), and we can prove this inductively.