Problem 8 Find $A \cup B$. $$A=\\{-3,-... [FREE SOLUTION]

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Chapter 14: Problem 8

Find $A \cup B$. $$A=\\{-3,-2,-1\\} ; B=\\{-2,-1,0\\}$$

Short Answer

Expert verified

$-3, -2, -1, 0$

Step by step solution

Analyze the sets

Identify the elements of set A which are -3, -2, -1 and those of set B which are -2, -1, 0.

Combine the elements

Combine the elements of both sets, resulting in the combined set: -3, -2, -1, -2, -1, 0. Though, -2 and -1 appear twice as they are in both sets A and B.

List unique elements

Represent the union of the sets A and B by listing the combined elements only once in the new set. Therefore, $A \cup B = \{-3, -2, -1, 0\}$

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Key Concepts

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

Sets

In mathematics, a set is essentially a collection of distinct objects or elements. When we talk about sets, we are referring to a basic fundamental concept in math that groups objects together based on a specific rule or criterion. These elements can be numbers, letters, symbols, or even other sets. For example, in set $A = \{-3, -2, -1\}$, the elements are the numbers -3, -2, and -1.
Sets are typically written in curly braces with elements separated by commas, and there should be no repetition among the elements. Several operations can be performed on sets, such as union, intersection, and difference, which allow us to explore relationships between different sets.

Union of Sets

The union of sets is a fundamental concept in set theory. It combines all the elements from two or more sets into a single set, ensuring that no duplicates are included. The symbol for union is $\cup$. If you have two sets, $A$ and $B$, their union, $A \cup B$, is a set containing all elements that are in $A$ or $B$ or in both.
For instance, if $A = \{-3, -2, -1\}$ and $B = \{-2, -1, 0\}$, to find $A \cup B$, you list all distinct elements once, resulting in $\{-3, -2, -1, 0\}$. Remember, even if an element appears in both sets, it is included in the union only once. This is a key property of the union operation: combining sets without repetition.

Elements of a Set

Elements of a set are the individual items or objects contained within that set. They are what make up the set itself. Each element in a set is unique, which means no element is repeated. This is a critical feature of a set鈥攄istinctiveness.
An element can be anything such as a number, word, symbol, or even another set, as long as it satisfies the criteria for being part of that particular set. For example, the elements of set $A = \{-3, -2, -1\}$ are simply the numbers -3, -2, and -1. The same rule applies to set $B = \{-2, -1, 0\}$. When we perform operations on sets, like finding a union, it's crucial to consider each element carefully to ensure accuracy.

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91影视

Find \(A \cup B\). $$A=\\{-3,-2,-1\\} ; B=\\{-2,-1,0\\}$$

Short Answer

Step by step solution

Analyze the sets

Combine the elements

List unique elements

Key Concepts

Sets

Union of Sets

Elements of a Set

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