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Chapter 10: Problem 22

How do you determine the number of elements in a set?

Short Answer

Expert verified
Answer: 6

Step by step solution

01

Definition of a Set

A set is a collection of distinct objects, also called elements or members, which are considered as a whole. Each object or element in the set is unique, i.e., no duplicates are allowed.
02

Identifying Elements in a Set

To identify the elements within a set, examine the set carefully, and make a list of all unique elements. Elements in a set are usually enclosed within curly brackets { } and separated by commas, denoting that they are part of the set. For example, the set {1, 2, 3, 4} has four distinct elements, which are the numbers 1, 2, 3, and 4.
03

Counting Elements in a Set

After identifying the distinct elements in the set, you can determine the number of elements in the set by simply counting them. The number of elements in a set is referred to as the cardinality of the set and is represented using the notation |A| or |S|, where A or S denotes the given set. Example: Let us determine the number of elements in the set A = {2, 3, 4, 7, 9}. Step 1: Identify the distinct elements in the set A. {2, 3, 4, 7, 9} Step 2: Count the number of distinct elements. There are 5 distinct elements in the set A. Step 3: Write the cardinality of the set. |A| = 5 In conclusion, there are 5 elements in the set A.

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