In Exercises 21–28, find the intersection of the sets. {a,b,c,d}∩∅

Key Concepts

Sets

A set is a collection of distinct objects, considered as an object in its own right. Sets are typically denoted by curly braces, such as {a, b, c, d}. Each element in a set is unique, and the order of elements does not matter. Understanding sets is fundamental in mathematics, particularly in topics like set theory, probability, and algebra.

Intersection of Sets

The intersection of two sets is a new set that contains all elements that are common to both sets. It is denoted by the symbol '∩'. For example, if we have sets A = {a, b, c} and B = {b, c, d}, then A ∩ B = {b, c}. The intersection is crucial for understanding relationships between sets and is often used in various mathematical applications.

Empty Set

The empty set, denoted by ∅, is a set that contains no elements. It is a fundamental concept in set theory, representing the idea of 'nothing' or 'no items'. When finding the intersection of any set with the empty set, the result is always the empty set, as there are no common elements. This concept is essential for understanding the properties of sets and their interactions.