How to Do Set Notation in Algebra

A set is a collection, just as "math" is a collection of letters.

Learning to use set notation in algebra means mastering the few symbols and understanding what each represents. Even without realizing it, you already think of things in sets. A baseball team is a set of players in which each player is an element or member of the set. Sets can be easy to understand if you apply the concept to everyday life.

Instructions

1. Enclose the elements (or members) of the set in curly brackets, {}. When there is nothing inside the brackets, it is called the "empty set." In writing sets, separate elements with commas. Examples of writing sets in algebra include: {1,2,3} or {x is a natural number; x < 4} You can also use a capital N to represent the natural numbers, just as Z represents integers, R represents real numbers and Q represents fractions. For the phrase "is an element of" you can use the symbol which looks like a curly E.

2. Use a U to represent the notation for union of two sets. To union both sets is to combine all the elements together. So {1,2,3,4} U {2,4,6,8} would produce the set {1,2,3,4,6,8} Note that you do not duplicate common elements.

3. Use the symbol for intersection to create a set of common elements. The symbol for intersection looks like an upside down U. So the intersection of {1,2,3,4} and {2,4,6,8} would be the set {2,4}.

4. Define one set to be a subset of another using a symbol that looks like a U placed on its side. A subset is a set in which every element of that set is contained within another set. Therefore the set {1,3} is a subset of {1,2,3,4}. If a set is not a subset, use the subset symbol with a diagonal slash drawn through it.

References

• Purplemath: Set Notation