In Exercises 21–28, find the intersection of the sets. {1,2,3,4}∩{2,4,5}

Key Concepts

Sets

A set is a collection of distinct objects, considered as an object in its own right. In mathematics, sets are often defined by listing their elements within curly braces, such as {1, 2, 3, 4}. Understanding sets is fundamental for operations like union, intersection, and difference, which are key to set theory.

Intersection of Sets

The intersection of two sets is a new set that contains all the elements that are common to both sets. It is denoted by the symbol '∩'. For example, the intersection of {1, 2, 3, 4} and {2, 4, 5} is {2, 4}, as these are the elements present in both sets.

Element Membership

Element membership refers to whether an object is a member of a set. This is often denoted using the symbol '∈'. For instance, in the set {1, 2, 3, 4}, the number 2 is an element, so we can say 2 ∈ {1, 2, 3, 4}. Understanding element membership is crucial for determining intersections and other set operations.