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