Set union and intersection operations constitute fundamental binary operations within the domain of set theory, governed by the axioms of Zermelo–Fraenkel set theory. These mechanisms define new sets containing elements present in one or both operands (union) or exclusively in both operands (intersection), utilizing formal notation such as $\cup$ and $\cap$. They serve as the algebraic basis for analyzing subset relationships, cardinalities, and the structural properties of collections without regard for element order or multiplicity.
Prerequisite chain context: requires Merging dictionaries in Python using pipe operator and update method.