# A calculus of the absurd

##### 18.3.4 The material bi-conditional

This is the operator which corresponds to the natural language statement “$$A$$ if and only if $$B$$”, which is to say that if $$A$$ is true, then $$B$$ must also be true (and vice versa). The basic idea is that $$A$$ and $$B$$ are concomitant; we cannot have one without the other.

• Definition 18.3.2 We define the logical operator $$A \iff B$$ using the following truth table,

 $$A$$ $$B$$ $$A \iff B$$ F F T F T F T F F T T T