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

Verified step by step guidance

1. Identify the elements in the first set: \( \{1, 2, 3, 4\} \).
2. Identify the elements in the second set: \( \{2, 4, 5\} \).
3. Determine which elements are common to both sets.
4. List the common elements found in both sets.
5. The intersection of the sets is the set of these common elements.

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.