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.
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