1.2.1 Set Theory

Key Objectives • Find the union and intersection of sets. • Make Venn diagrams and find complements of sets. • Determine relationships between sets. • Find the cross product of sets. Key Terms • A set is a collection of items called elements. • An element is an item in a set. • The intersection of two sets is the set of all elements that are found in both sets. The intersection of sets is denoted by ∩ . • The union of two sets is the set of all elements that are found in either set. The union of sets is denoted by ∪ . • The empty set is the set that contains no elements. The empty set is denoted by ∅ or {}. • The universe (universal set) for a particular situation is the set that contains every element relating to the situation. • The complement of set A in universe U is the set of all elements in U that are not in set A . • A subset is a set that is contained entirely within another set. Set B is a subset of set A if every element of B is contained in A , denoted B ⊆ A . • The cross product of two sets A and B is the set of ordered pair elements ( a , b ), where a is an element of A and b is an element of B . The cross product of sets A and B is denoted by A × B . Example 1 Finding the Union and Intersection of Sets Sets are collections of items, called elements, are commonly named with uppercase letters, such as A and B . The union of two sets A and B , denoted A ∪ B , is the set of all elements that are in either set A or in set B . The intersection of two sets A and B , denoted A ∩ B , is the set of all elements common to both sets A and B . If two sets have no elements in common, then their intersection is the empty set, denoted ∅ or {}.

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