How is the intersection and the union 100

In mathematical terms, intersection is simple and simple, and it can be understood in this way, the same has the same property and is essentially called the part with intersection. Union is the combination of the same, the same, and the different.

Intersection is the part that you and I have, and union is the whole of us.

In general, a set of all elements that belong to set A or set B is called the union of set A and set B.

An intersection is something that can intersect, there is the same, and a union is a combination.

When you look at books, definitions are important.

First, the nature is different.

1. Union: A and B are combined together to form a set.

2. Intersection: A set of all elements that belong to set A and belong to set B.

Second, the way of representation is different.

1. Union: denoted as a b, read as a and b.

2. Intersection: Recorded as A B, read as "the intersection of A and B".

Third, the characteristics are different.

1. Union: The union operation makes any power integration into a Boolean algebra.

2. Intersection: The number 9 does not belong to the intersection of the set of prime numbers and the set of odd numbers.

The difference between union and intersection is:The nature is different, the essence is different, and the expression is different

1. The nature is different.

Intersection is the gathering or interweaving of different things or feelings; Union is the common thing that two things contain. Mathematically, in general, for a given set of two sets A and the intersection of sets B means the inclusion of all elements belonging to both A and B, and in set theory and other branches of mathematics, the union of a set of sets is the set of all the elements of these sets and contains no other elements.

2. The essence is different.

The intersection is the crossing; Union is plus. An intersection is a part that two sets have in common, but it means that all of them have work. Union is when two sets are combined to form a common set, in the form of x belongs to a b if and only if x belongs to a and x belongs to b.

3. Representation is different.

Writing at the intersection of A and B"a∩b", a b= a and b are combined to write "a b", i.e. a b=.

Intersection operations

1) If the intersection of two sets a and b is empty, then they say they have no common element, writing: a b = e.g. set and disjoint, writing

2) The intersection of any set with an empty set is an empty set, i.e. a =

3) More generally, intersection operations can be performed on multiple sets at the same time. For example, the intersection of sets a, b, c, and d is a b c d=a [b (c d)]. The intersection operation satisfies the associative property, i.e., a(b c)=(a b) c.

4) The most abstract concept is the intersection of sets of arbitrary non-empty sets. If m is a non-empty set whose elements are also sets themselves, then x belongs to the intersection of m, and if and only if for any element a of m, x belongs to a. This concept is the same as the idea described above, e.g., a b c is the intersection of sets (it is sometimes possible to figure out when m is empty, see Empty Intersection).

The notation of this concept also changes from time to time. It is sometimes used by set theorists"∩m", sometimes used"∩a∈ma"。The latter can be generalized as:"∩i∈iai", which represents the intersection of the set .

Here i is non-null and ai is a set of i belonging to i.

Intersection. Representation means the same element in two sets, memorization method: the symbol that intersects is a round arch.

And guess the band set: the representation method, which means to take all the elements of the two sets, and memorize the method: the symbol of the union is that the door is reversed.

Example: 1) The intersection of the set {1,2,3} and {2,3,4} is {2,3}. i.e. {1,2,3} {2,3,4}=.

2) The number 9 is not a prime number.

Set {2,3,5,7,11, ..)and odd sets {1,3,5,7,9,11, ..)of the intersection. i.e. 9 {x|x is a prime number} {x|x is an odd number}.

Operations

Intersection of the shape of the operation:

a∩b=b∩a

a a Huai Zhao rent a = a

a∩b⊆a，a∩b⊆b

a∩b=a⇔a⊆b

a b= , the two sets do not have the same element.

a∩（∁ua）＝∅

u（a∩b）＝（ua）∪（ub）

The arithmetic shape of the union:

a∪b=b∪a

a∪∅＝aa∪a=a

a∪b⊇a，a∪b⊇b

a∪b=b⇔a⊆b

a b= , both sets are empty sets.

a∪（cua）＝u

cu（a∪b）＝（cua）∩（cub）

Intersection: In set theory, let a and b be two sets, and the set composed of all the elements that belong to set a and belong to set b is called the intersection of set a and set b. Namely:

a∩b=。Written as a b, it is read as "the intersection of a and b". Note that when the symbol is written before the other symbols, not between, it needs to be written one size larger.

Union: If A and B are sets, then A and B unions are sets of all A elements and all B elements, and no other elements. The union of a and b is usually written"a∪b", pronounced "a and b", is represented in symbolic language, i.e.:

a∪b=。Formally, x is an element of a b, if and only if x is an element of a, or if x is an element of b.

Intersection: Representation method

Union : Representation method

In set theory, let a and b be two sets, and the set composed of all the elements that belong to set a and belong to set b is called the intersection of set a and set b, which is denoted as a b.

A b means that A intersects B, i.e., the common part of Set A and Set B. AUB means A and B, i.e. all of Set A and Set B.

For example: two sets a, b.

Then a b denotes the elements common to the set ab, i.e.

aub represents two sets of all the elements, and the common cosmetic is counted only once, ie.

Expand the information of the Lu Leak Li Zhan:

Nature of Intersection :

1) If the intersection of two sets A and B is empty, then they are said to have no common element, write: A b =

2) The intersection of any set with an empty set is an empty set, i.e. a =

Nature of union:

1) An empty set is a unit element of union operations. i.e. a=a. For any set a, you can use the empty set search as the union of zero sets.

Union and intersection satisfy each other's distributive laws, and these three operations satisfy de Morgan's laws. If you replace the union operation with a symmetry difference operation, you can obtain the corresponding Boolean ring.

<>A b represents the union (set) of two events, A and B, (the two elliptical circles in the figure represent event A and event B, respectively, and the two have intersecting parts), and the probability P(A B) is the probability that event A occurs or Event B occurs, or that both A and B occur at the same time.

ab represents the intersection (set) of a and b, (i.e., the part of the graph where a and b intersect), and its probability p(ab) is the probability that event a and event b occur at the same time.