# Contingency

In logic, a contingency is a proposition that may be either true or false, and is not necessarily one or the other.

For example, the proposition “Sam is wearing a hat” is a contingency — it is not always or neccessarily the case that Sam is wearing a hat. The proposition is said to be contingent on whether or not Sam is, in actuality, wearing a hat.

The contingency of propositions is not normally an issue in propositional or first-order logic, but in modal logic, there is an important distinction there. However, contingency of formulae is universally important, as it distinguishes normal formulae from tautologies and contradictions.

## Contingent Formulae

In propositional logic, a formula is said to be contingent when it may be either true or false, depending on the valuation of its terms.

For example, the formulas ¬A and A ∨ B are both contingent. On the valuation A=True, B=False, the first formula is false and the second is true. On the valuation A=False, B=False, then the first formula is true and the second is false.

A contingent formula may be contrasted with a tautology, which is always true, or a contradiction, which is never true.