What is the difference between subset and universal set

If the universal set contains sets A and B, then and. Directions: Read each question below. Select your answer by clicking on its button. If you make a mistake, rethink your answer, then choose a different button. By signing up, you agree to receive useful information and to our privacy policy. Shop Math Games. Skip to main content. Search form Search. Answer: A and B have no elements in common. These sets do not overlap. The procedure for creating a Venn diagram is as follows; Draw a rectangle and label it U to represent the universal set.

Draw circles within the rectangle to represent the subsets of the universe. Label the circles and write the relevant elements in each circle. Write the remaining elements outside the circles but within the rectangle. Let's look at some more examples. Answer: In example 3, subsets P and Q are overlapping. Answer: In example 5, subsets X and Y do not overlap. Answer: In example 6, Band and Chorus are overlapping sets.

Exercises Directions: Read each question below. Introduction to Sets. Basic Set Notation. Types of Sets. Set Equality. Venn Diagrams. Universal Set. Set-Builder Notation. Practice Exercises. Challenge Exercises. The universal set, denoted by U, is a set or the larger set that contains elements of all the related sets, that too without any repetition of elements. The elements in the universal set are not repeated, thus they are unique.

In this article, let's learn about the universal set, its definition, representation with solved examples. The universal set is a collection of all elements or members of all the related sets, known as its subsets. All the stars in a milky way galaxy is a good example of a universal set if we consider all the stars in the milky way galaxy. When we study numbers in mathematics, we are interested in the set of natural numbers.

This basic set is considered a universal set and its subsets are even numbers , prime numbers , etc. The universal set is the set of all elements or members of all related sets. It is usually denoted by the symbol E or U. For example, in human population studies, the universal set is the set of all the people in the world.

The set of all people in each country can be considered as a subset of this universal set. The universal set is usually represented by the symbol E or U. It consists of all the elements of its subsets, including its own elements. Let's consider an example with three sets, A, B, and C. We need to find the universal set for all three sets A, B, and C. All the elements of the given sets are contained in the universal set. Thus, the universal set U of A, B, and C is given by:.

We can see that all the elements of the three sets are present in the universal set without any repetition. Thus, we can say that all the elements in the universal set are unique. The sets A, B, and C are contained in the universal set, then these sets are also called subsets of the Universal set. For a subset A of the universal set U , its complement is represented as A' which includes the elements of the universal set but not the elements of set A.

The Universal set consists of a set of all elements of all its related subsets, whereas the empty set contains no elements of the subsets.

Most of the time we use the Venn diagram to show the relationship between sets. Venn diagrams are the graphical representation of the sets. The universal set is represented by a rectangle and its subsets are represented by circles. Usually, students have confusion in differentiating between the union of the set and the universal set. We can understand the difference better by looking at their definitions.

The following example can be used to understand this difference better. Let's find the universal set U and the union of sets A and B. Thus, we can see that the universal set contains the elements from A, B, and U itself, whereas the union of A and B contains elements from only A and B.

Example 1: Given below is a Venn diagram representing the sets, A and B. Determine the elements of the universal set for its given subsets, A and B. We know that any universal set is represented by a rectangle and its subsets are represented by circles.

Clearly, A and B are disjoint sets because they have no common element. Also, the elements that are not contained in A and B are contained in the universal set.