Go backward to Operational Interpretation Go up to Top Go forward to Conjunctions

Inversion of Negation

Proposition: For every formula A, we have

~~A iff A.

Proof: Let A be an arbitrary formula. We have to show that the meaning of ~~A is the same as the meaning of A, i.e., that they have the same truth values.

A	~A	~~A
false	true	false
true	false	true

Since the last column coincides with the first column, we are done.