Set Operations

The set operations are the union, intersection, and difference of sets. The union of two sets is the set of all elements that are in either set. The intersection of two sets is the set of all elements that are in both sets. The difference of two sets is the set of all elements that are in the first set but not in the second set.

What is the Data Set?

The data set is a table that includes the percentage of people who are obese in each U.S. state in 2011.

Notation

The notation used in this problem is the standard mathematical notation for a vector. A vector is a set of numbers, usually represented by an arrow, that has a magnitude (length) and a direction. In this problem, the vector is represented by the three numbers (5, -2, 3), which represent the magnitude and direction of the vector.

Representation of A Set

A set is a collection of objects. The objects in a set can be anything: numbers, letters, colors, shapes, etc.

There are two ways to represent a set:

1. List the objects in the set

2. Use a symbol to represent the set

Listing the Objects in a Set

If we want to list the objects in a set, we use a comma-separated list.

For example, the set {1, 2, 3} can be written as:

1, 2, 3

or

1, 2, 3

Using a Symbol to Represent a Set

If we want to use a symbol to represent a set, we use a curly bracket.

For example, the set {1, 2, 3} can be written as:

{1, 2, 3}

or

{1, 2, 3}

Types of Sets

There are three types of sets:

1. Finite sets

2. Infinite sets
3. Ordered sets

Finite sets are sets that have a finite number of elements. Infinite sets are sets that have an infinite number of elements. Ordered sets are sets that have a specific order to their elements.

Union of Sets

The union of two sets is the set of all elements that are in either set.

The union of set A and set B is the set {x | x ∈ A or x ∈ B}.

For example, the union of the set of numbers 1, 2, and 3 is the set {1, 2, 3}.

Intersection of Sets

The intersection of two sets is the set that contains all the elements that are in both sets.

For example, the intersection of the sets {1, 2, 3} and {4, 5, 6} is the set {4, 5, 6}.

Difference of Sets

The difference of two sets is the set of all elements that are in the first set but not in the second set.

For example, the difference of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3}.

Properties of Set Operations

Union

The union of two sets is the set of all elements that are in either set.

Example:

The union of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3, 4, 5, 6}.

Intersection

The intersection of two sets is the set of all elements that are in both sets.

Example:

The intersection of the sets {1, 2, 3} and {4, 5, 6} is the set {4, 5}.

Complement

The complement of a set is the set of all elements that are not in the set.

Example:

The complement of the set {1, 2, 3} is the set {4, 5, 6}.

Union of Sets

“The union of sets is the set of all elements that are in either set.”

The union of two sets, A and B, is the set of all elements that are in either set A or set B. The union of A and B is written as A ∪ B.

For example, the union of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3, 4, 5, 6}.

Intersection of Sets

The intersection of two sets is the set of all elements that are in both sets.

For example, the intersection of the sets {1, 2, 3} and {4, 5, 6} is the set {4, 5, 6}.