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Chapter 4: Problem 24

Find each indicated intersection or union. $$ \\{m, n, o, p\\} \cap\\{m, o, p\\} $$

Short Answer

Expert verified
The intersection is \(\{m, o, p\}\).

Step by step solution

01

- Identify the Sets

Examine the two sets given in the problem. The first set is \(\text{\{m, n, o, p\}}\) and the second set is \(\text{\{m, o, p\}}\).
02

- Understand Intersection

The intersection of two sets includes all the elements that are present in both sets. This means we need to find elements that are common to both \(\text{\{m, n, o, p\}}\) and \(\text{\{m, o, p\}}\).
03

- Find Common Elements

Compare the elements of the two sets. The common elements are `m`, `o`, and `p`.
04

- Write the Intersection

The intersection of the two sets \(\text{\{m, n, o, p\}}\) and \(\text{\{m, o, p\}}\) is \(\text{\{m, o, p\}}\).

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Key Concepts

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

Union of Sets
The union of two sets is a fundamental concept in set theory. It combines all the unique elements from both sets into a single set. It's denoted using the symbol 鈭�. For example, if we have sets \{m, n, o, p\} and \{m, o, p\}, the union combines these elements. But remember, duplicates are removed in a union. So, if both sets contain `m`, it only appears once in the union.
In mathematical notation, it looks like this: \[\{m, n, o, p\} 鈭� \{m, o, p\} = \{m, n, o, p\}\]. Notice how `m`, `o`, and `p` do not repeat even though they are in both sets. This is an important aspect to remember. Use the union operation to find all unique elements across given sets.
Common Elements
Finding common elements between sets is key to understanding their intersection. The intersection of two sets, denoted by 鈭�, includes all elements that appear in both sets.
For the given sets \{m, n, o, p\} and \{m, o, p\}, we need to identify the elements that are present in both. Begin by listing out elements of each set:
  • Set 1: `m`, `n`, `o`, `p`
  • Set 2: `m`, `o`, `p`
Next, look for elements that appear in both lists. Here, `m`, `o`, and `p` are common to both sets.
Therefore, the intersection is written as \[\{m, o, p\}\]. This tells us which elements are shared between the two sets. Use intersections to determine shared elements in studies like data analysis and databases.
Mathematical Notation
Understanding how to read and write mathematical notation is vital for solving set theory problems. When working with sets, we often use symbols to represent operations. Some common symbols include:
  • 鈭�: Union, combines all elements from both sets
  • 鈭�: Intersection, finds common elements between sets
  • \{\}: Curly brackets, enclose elements of a set
In the problem we solved, we used these notations:
1. Identified the sets: \[\{m, n, o, p\}\] and \[\{m, o, p\}\]
2. Found the intersection (common elements): \[\{m, o, p\}\]
Always write clearly, understand symbols, and match elements accurately when using mathematical notation. Practice with problems to become more comfortable.

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