Some truth functions possess properties which may be expressed in the theorems containing the corresponding connective. Some of those properties that a binary truth function (or a corresponding logical connective) may have are:
*'''[[Associativityassociativity]]''': Within an expression containing two or more of the same associative connectives in a row, the order of the operations does not matter as long as the sequence of the operands is not changed.
*'''[[Commutativitycommutativity]]''': The operands of the connective may be swapped without affecting the truth-value of the expression.
*'''[[Distributivitydistributivity]]''': A connective denoted by · distributes over another connective denoted by +, if ''a'' · (''b'' + ''c'') = (''a'' · ''b'') + (''a'' · ''c'') for all operands ''a'', ''b'', ''c''.
*'''[[Idempotenceidempotence]]''': Whenever the operands of the operation are the same, the connective gives the operand as the result. In other words, the operation is both truth-preserving and falsehood-preserving (see below).
*'''[[Absorptionabsorption Law|Absorption]]''': A pair of connectives <math>\land, \lor</math> satisfies the absorption law if <math>a\land(a\lor b)=a</math> for all operands ''a'', ''b''.
A set of truth functions is [[functional completeness|functionally complete]] if and only if for each of the following five properties it contains at least one member lacking it:
