Problem 33 In Exercises $29-34,$ find the... [FREE SOLUTION]

Chapter 0: Problem 33

In Exercises $29-34,$ find the union of the sets. $$\\{a, e, i, o, u\\} \cup \varnothing$$

Short Answer

Expert verified

The union of the sets \{a, e, i, o, u\} and \varnothing\ is \{a, e, i, o, u\}.

Step by step solution

Identify the Elements of the Given Sets

The given sets are: Set A = \{a, e, i, o, u\} and Set B = \varnothing\. So, Set A contains the vowels and Set B is an empty set.

Apply the Union Operation

The union of two sets, denoted as A 鈭� B, is the set of all elements that are in set A, or in set B, or in both. In this case, as set B is an empty set, it does not add any new elements to the union. So, the union of the given sets is the same as the set of vowels.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Union of Sets

The union of sets is a fundamental concept in set theory, which deals with the combination of elements from different sets. If you have two sets, their union is essentially all elements present in either of the sets or both. Let's say set A has the elements $\{1, 2, 3\}$ and set B has the elements $\{3, 4, 5\}$. The union of set A and set B, represented as $A \cup B$, would be $\{1, 2, 3, 4, 5\}$.

This is because all elements in A or B, or both, are included in the union
The union operation does not repeat elements; each unique element is only listed once in the resulting set

Remember, the union of any set with the empty set will always result in the original set. This is because there are no elements in the empty set to add to the union.

Empty Set

An empty set, often represented with the symbol $\varnothing$ or sometimes $\{ \} $, is a set that contains no elements at all. It is a very special set in mathematics and serves as the basis for starting operations in set theory.

Whenever a set operation includes the empty set, it typically results in the other operand
That is because the empty set contributes no elements whatsoever

For example, if you take a set of numbers $\{2, 4, 6\}$ and find its union with the empty set, the union remains $\{2, 4, 6\}$. Similarly, any set intersecting with the empty set will result in an empty set since there is no overlap.

Vowels Set

The vowels set is a simple concept where we have a specific group of elements that represent vowels found in the English language. Generally, when we talk about a vowels set in exercises or problems, it includes these specific five vowels: $\{a, e, i, o, u\}$.

These are typically viewed as a set because they are distinct elements that are grouped together by a common property
The order in which we list the elements of a set does not change the set, so $\{a, e, i, o, u\}$ is the same set as $\{u, o, a, e, i\}$

When experimenting with operations such as union or intersection, the vowels set often serves as a rich and straightforward example, as it contains familiar and distinct elements.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Exercises \(29-34,\) find the union of the sets. $$\\{a, e, i, o, u\\} \cup \varnothing$$

Short Answer

Step by step solution

Identify the Elements of the Given Sets

Apply the Union Operation

Key Concepts

Union of Sets

Empty Set

Vowels Set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Pure Maths

Statistics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.