Problem 2 Complete each statement using th... [FREE SOLUTION]

91影视

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 4: Problem 2

Complete each statement using the word intersection or the word union. The symbol U indicates _____.

Short Answer

Expert verified

The symbol U indicates union.

Step by step solution

- Understanding the Symbols

In set theory, each symbol has a specific meaning. The two symbols we are dealing with here are 'U' and '鈭�' (intersection). Let's focus on the symbol 'U'.

- Union in Set Theory

The 'U' symbol stands for 'union'. In set theory, the union of two sets is a set that contains all the elements from both sets combined.

- Completing the Statement

The given statement is: 'The symbol U indicates ____.' By our understanding, the statement is completed by saying: 'The symbol U indicates union'.

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Key Concepts

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

Set Theory

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. Objects in a set are called elements. Sets are used to group related objects together into a single entity. Here's some important terminology:

Elements: Objects within a set.
Subset: A set whose elements are all contained in another set.
Empty Set: A set with no elements, denoted as $otin$.

In set theory, we often use symbols to describe relationships between sets and their elements:

Union

The concept of union in set theory is indicated by the symbol 'U'. When we talk about the union of two sets, we mean a new set that contains every element that is in at least one of the original sets. For example, if we have:

Set A = \{1, 2, 3\}
Set B = \{3, 4, 5\}

Then, the union of sets A and B, denoted as $A \cup B$, is:
$A \cup B = \{1, 2, 3, 4, 5\}$, combining all unique elements from both sets.

Intersection

The concept of intersection in set theory is denoted by the symbol '鈭�'. The intersection of two sets is a new set containing elements that are in both of the original sets. For example, consider:

Set A = \{1, 2, 3\}
Set B = \{2, 3, 4\}

Then, the intersection of sets A and B, denoted as $A \cap B$, is:
$A \cap B = \{2, 3\}$
This set only includes elements that appear in both sets.

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91影视

Complete each statement using the word intersection or the word union. The symbol U indicates _____.

Short Answer

Step by step solution

- Understanding the Symbols

- Union in Set Theory

- Completing the Statement

Key Concepts

Set Theory

Union

Intersection

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