The formulas `A`

and `B`

are said to be *equivalent*, written `A ⇔ B`

,
if they are both satisfied by the same truth assignments.
The formula `A ⇔ B`

is equivalent to `A ⇒ B ∧ B ⇒ A`

which is also equivalent to
`(¬A ∨ B) ∧ (A ∨ ¬B)`

.

The truth table below shows all possible combinations for an equivalence.
Here `t`

stands for true, and `f`

stands for false.

` A ` | ` B ` | ` A ⇔ B ` |
---|---|---|

`f` | `f` | `t` |

`f` | `t` | `f` |

`t` | `f` | `f` |

`t` | `t` | `t` |

Doets, Kees. *From Logic to Logic Programming.* MIT Press, 1994.

Copyright © 2014 — 2016 Barry Watson. All rights reserved.