Union and Intersection of Sets of Cardinal Numbers

# Union and Intersection of Sets of Cardinal Numbers

## Cardinal Number of a Set

A cardinal number is the number of elements in a set. For example, the cardinal number of the set {1, 2, 3} is 3.

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## a Union b

A union is a collection of data that can be treated as a single entity. The data in a union can be of different types, but they are all stored in the same location. When you access the data in a union, you access all of it at the same time.

## a Union b Formula

A union is a type of data structure that allows two or more different data types to be stored in a single variable. The union is defined by a single variable, which can store a value of any of the data types that are included in the union.

The following example defines a union that includes the data types int, double, and string.

union MyUnion
{

int i;
double d;
string s;

}

The union can be initialized with a value of any of the data types that are included in the union.

MyUnion u = {10, 3.14, “Hello”};

The following code uses the union to store a value of type int.

u.i = 5;

The following code uses the union to store a value of type double.

u.d = 6.28;

The following code uses the union to store a value of type string.

u.s = “World!”;

## a Intersection b

Intersection c Intersection d Intersection

1 a, b, c
2 a, b, c, d
3 a, b, c, d, e
4 a, b, c, d, e, f
5 a, b, c, d, e, f, g
6 a, b, c, d, e, f, g, h
7 a, b, c, d, e, f, g, h, i
8 a, b, c, d, e, f, g, h, i, j
9 a, b, c, d, e, f, g, h, i, j, k
10 a, b, c, d, e, f, g, h, i, j, k, l

## a Intersection b Formula

: a ∩ b = {x : a = x and b = x}

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

## Union and Intersection of Three Sets

If three sets are intersecting, then the intersection is the set of all elements that are in two or more sets.

If three sets are unioned, then the union is the set of all elements that are in any of the sets.

## Union and Intersection of Three Sets Formula

The intersection of three sets is a set that is composed of the elements that are common to all three sets. The union of three sets is a set that is composed of the elements that are in any of the three sets.

The intersection of three sets can be represented using a Venn diagram. The union of three sets can be represented using a Venn diagram as well. However, in a Venn diagram, the union of three sets is represented by a single circle that contains the elements that are in any of the three sets.

## Probability Union and Intersection

The union of two sets A and B, denoted by A ∪ B, is the set of all elements that are in either A or B, or both. The intersection of two sets A and B, denoted by A ∩ B, is the set of all elements that are in both A and B.

The following Venn diagrams illustrate the union and intersection of two sets:

In the first diagram, the set A is represented by a circle and the set B is represented by a rectangle. The union of A and B is represented by the overlapping area of the circle and the rectangle.

In the second diagram, the set A is represented by a triangle and the set B is represented by a square. The intersection of A and B is represented by the overlapping area of the triangle and the square.

## Venn Diagram Union and Intersection Problem Example

In this Venn diagram union and intersection problem example, we will be looking at a problem that involves two overlapping circles.

The problem states that there are a total of ten students in two classes, and that four students are in both classes.

We can represented this problem using a Venn diagram as follows:

From the diagram, we can see that there are a total of ten students, and that four of those students are in both circles. This means that the intersection of the two circles is equal to four students.

We can also see that the union of the two circles is equal to six students. This means that the two circles overlap, but do not intersect.