A binary logical connective, denoted

\[\begin{equation*} P \iff Q \qor P \equiv Q, \end{equation*} \]

and read

“\(P\) if and only if \(Q\)” | |

or | “\(P\) is equivalent to \(Q\)”, |

that is ‘`true`’ if and only if

which is equivalent to

\[\begin{equation*} (P \implies Q) \> \land \> (Q \implies P). \end{equation*} \]

(Levin, 2021, sec. 0.2; Poole & Mackworth, 2017, sec. 5.1)

Construct the truth table for the statement

\[\begin{align*} P \iff Q \> & \equiv \> (P \implies Q) \land (Q \implies P) \\ & \equiv \> (\lnot P \lor Q) \land (\lnot Q \lor P). \end{align*} \]

<<scheme/org-truth-table>> (org-truth-table (lambda (p q) (and (or (not p) q) (or (not q) p))) '("P" "Q" "P \\iff Q"))

\(P\) | \(Q\) | \(P \iff Q\) |
---|---|---|

false | false | true |

false | true | false |

true | false | false |

true | true | true |

© 2024 Rudolf Adamkovič under GNU General Public License version 3.

Made with Emacs and secret alien technologies of yesteryear.