👉 Unions, in the context of mathematics, particularly in set theory and logic, are a way to combine multiple sets into a single set while preserving certain properties. Formally, given two sets \( A \) and \( B \), the union \( A \cup B \) is a set containing all elements that are in \( A \), in \( B \), or in both. This operation is commutative and associative, meaning \( A \cup B = B \cup A \) and \( (A \cup B) \cup C = A \cup (B \cup C) \). Unions are fundamental in defining larger sets from smaller ones and are crucial in various mathematical structures, including Boolean algebras and topology. They help in expressing conditions that involve the combination of multiple elements or properties, making them a powerful tool for logical and set-based reasoning.
