> Two sentences, P and Q, are truth-functionally equivalent if and only if there is no truth assignment in which P is true and Q is false
### Informal expression
````
P: If it is raining then the pavement will be wet.
Q: The pavement is not wet unless it is raining.
````
### Formal expression
$$
P \supset Q \equiv \sim P \lor Q
$$
### Truth-tables
````
P Q P ⊃ Q
T T T
T F F
F T T
F F T
````
````
P Q ~ P ∨ Q
T T T
T F F
F T T
F F T
````
### Derivation
>
> Propositions $P$ and $Q$ are equivalent in a system of [derivation](Formal%20proofs%20in%20propositional%20logic.md) for propositional logic if $Q$ is derivable from $P$ and $P$ is derivable from $Q$.
Note that the property of equivalence stated in terms of derivablity above is identical to the derivation rule for the [material biconditional](Biconditional%20Introduction.md):
//TODO: Add demonstration of this by deriving two equivalents from one of DeMorgan's Laws
