## Introduction

### Definition

is included as a subordinate relationship between collections and collections, also called subset relationships. Basic meaning is in the same way, inclusion, incubation, and relationship adjectives. From Han · Guanxi "Salt Tribody · Vigorine": "The king contains parallel, love is selfless, not for near-researchers, not far-reaching."

### Classification

(1) is included in (including)

(2) true inclusion (true inclusive)

### properties

(1) Transmitability: If set A is included in the set B, the set B is included in the collection C, then the set A is included in the collection C.

(2) Nature: Collection A is included in the collection B, then the set A is in the collection B, belongs to B.

## Probability Nourse

### Introduction

actually encounters many events in a random phenomenon, and there are three relationships between them.

(1) contains:

There are two events A and B in a random phenomenon. If any of the sample points in event A must be in B, the A is included in B, or B includes A, which is "a contained in B": A⊂B or "B contains A": B⊃A, At this time, the occurrence of event A must cause event B. As shown on the right. Such as throwing a dice, event a = "4 points" must cause event B = "Apostable point", so A⊂B.

(2) Mutual incompatibility:

There are two events A and B in a random phenomenon. If events A is not the same sample point, the events A and B are incompatible. At this time, events A and B cannot occur at the same time. As shown in Figure 1, such as "TV service life is less than 10,000 hours" in the TV life test, "TV service life is more than 40,000 hours" is two mutually incompatible events because they have no sample points? Or Say that they can't happen simultaneously.

The inter-incompatibility between the two events can be extended to three or more events. For example, when checking three products, C1 = "just a unqualified product", C2 = "There is two unqualified products", C3 = "all unqualified products", c0 = "There is no unqualified product" Four mutually incompatible events.

(3) Equal:

There are two events A and B in a random phenomenon. If events A and B contain the same sample point, the events A is equal to B, and it is recorded as A = B. In the random phenomenon of two dice, its sample points are (x, y), where x and y are the number of points that appear in the first and second dices, and the following two events: a = {(x, Y): x + y = odd number}, b = {(x, y): X and Y 's parity difference}, can verify A and B contain the same sample point, so A = B.

### Examples

Elements and collections are called "belong to", and cannot be included, including only the collection and collection.

Example A = {1, 2}, b = {1, 2, 3}

1 ∈ A, 2∈A, 3∈B

Belongs to the relationship between elements and collections, for example, element A belongs to a collection A, records a ∈A

belonging to symbol: ∈, used between elements and collections

The inclusion between the collection and the collection is called the

if any of the elements of the set A is the element of the set B, then the set A is called the subset of collections B, which is recorded as B or B contains. A

empty set is included in any set, that is, the subset of any set

If the elements of the set A are the subset of collections B, at least one The elements are not A, then the collection A is called the true subset of collections B, which is referred to as a true inclusion of B or B true contains A.