# Satisfiability

We say that a logical statement is *satisfiable* when there exists at least one truth assignment that makes the overall statement true.

In our Logika truth tables, this corresponds to statements that are either *contingent* or a *tautology*. (*Contradictory* statements are NOT satisfiable.)

For example, consider the following truth tables:

```
*
-----------------------
p q r # p →: q V ¬r ∧ p
-----------------------
T T T # T T F F
T T F # T T T T
T F T # F F F F
T F F # T T T T
F T T # T T F F
F T F # T T T F
F F T # T F F F
F F F # T F T F
------------------------
Contingent
T: [T T T] [T T F] [T F F] [F T T] [F T F] [F F T] [F F F]
F: [T F T]
```

And

```
*
------------
p # p V ¬p
------------
T # T F
F # T T
-------------
Tautology
```

Both of these statements are satisfiable, as they have at least one (or more than one) truth assignment that makes the overall statement true.