Sentences with UNIVERSAL-SET

"In set theory, a universal set is a set that contains all the elements or objects under consideration."

"The universal set is usually denoted by the symbol U."

"For example, let's consider the universal set of all lowercase letters."

"The universal set in this case would be {a, b, c, d, ... , x, y, z}."

"A universal set can also be defined based on a specific context, such as all the students in a school."

"In that case, the universal set would be the set of all students at the school."

"The concept of a universal set is often used in conjunction with set operations like union and intersection."

"One property of a universal set is that every set is a subset of the universal set."

"Another property is that the complement of the empty set is equal to the universal set."

"In Venn diagrams, the universal set is represented by the rectangle that encloses all other sets."

"The universal set is infinite for some cases, such as the set of all real numbers."

"A universal set can be finite as well, like the set of all days in a week."

"In probability theory, the universal set represents the sample space of all possible outcomes."

"To define a universal set, one must clearly specify the elements or objects under consideration."

"The concept of a universal set is fundamental to the study of sets and their properties."

"Set theory provides a foundation for many areas of mathematics using the notion of a universal set."

"In some cases, it is not possible or necessary to define a universal set."

"The concept of a universal set can be extended to other fields like computer science and linguistics."

"The universal set is a way to encompass all possible elements in a given context."

"Understanding the concept of a universal set is essential for analyzing and manipulating sets."