In Exercises 1–6, 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

Set Theory

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. In this context, sets are defined by their elements, and operations can be performed on them, such as union, intersection, and difference. Understanding set theory is essential for solving problems involving collections of numbers or objects.

Intersection of Sets

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

Element Membership

Element membership refers to whether a particular object is a member of a set. This concept is fundamental in set theory, as it allows us to determine if an element belongs to a set when performing operations like intersection. For instance, in the sets {1, 2, 3, 4} and {2, 4, 5}, we check each element to see if it appears in both sets to find the intersection.