 Let \(\Omega\) be a set of possibilities that are mutually exclusive and jointly exhaustive. There is no restriction on the size of \(\Omega\); it can be finite or infinite. Let \(\cal A\) be a set of propositions identified with some subsets of \(\Omega\). Assume that \(\cal A\) contains \(\Omega\) and the empty set \(\varnothing\), and is closed under the standard Boolean operations: conjunction (intersection), disjunction (union), and negation (complement). This closure assumption means that, whenever \(A\) and \(B\) are in \(\cal A\), so are their intersection \(A \cap B\), union \(A \cup B\), and complement \(\Omega \mcomplement A\), which are often written in logical notation as conjunction \(A \wedge B\), disjunction \(A \vee B\), and negation \(\neg A\). When \(\cal A\) satisfies the assumption just stated, it is called an algebra of  sets/propositions.[2]