Use set notation, and list all the elements of each set. {12, 13, 14,..., 20}

Verified step by step guidance

1. Identify the set given: {12, 13, 14, ..., 20}. This set includes all integers starting from 12 up to 20.
2. Understand that the ellipsis (...) means the set contains all consecutive integers between the first and last numbers listed.
3. List all the elements explicitly by writing out each integer from 12 to 20: 12, 13, 14, 15, 16, 17, 18, 19, 20.
4. Write the set in set notation by enclosing all these elements in curly braces: {12, 13, 14, 15, 16, 17, 18, 19, 20}.
5. Confirm that the set includes only these integers and no others, as the problem specifies the range from 12 to 20.

Key Concepts

Set Notation

Set notation is a way to describe a collection of distinct objects, called elements, using curly braces {}. Elements inside the braces are listed or described by a rule. For example, {1, 2, 3} lists elements explicitly, while {x | x > 0} describes elements by a condition.

Listing Elements of a Set

Listing elements means writing out all members of a set explicitly. When given a range or pattern, you identify each element that fits the criteria and write them separated by commas inside braces. For example, {12, 13, 14, ..., 20} means all integers from 12 to 20 inclusive.

Understanding Ellipsis (...) in Sets

The ellipsis (...) indicates a continuation of a pattern in a set. It shows that elements follow a sequence without listing every element. To list all elements, you replace the ellipsis with the missing elements that continue the pattern, ensuring the set is complete.