What is the difference between union and intersection, I don t understand it in the book

Given two sets A and B, the set that merges all their elements together is called the union of set A and set B, denoted as a b, and read as a and b.

For example, the union of the set and is .

The set of all the elements that belong to set A and belong to set B is called the intersection of set A and set B, and is denoted as A B.

For example, the intersection of the set and is . i.e. =.

One is equivalent to the sum union, and the other is the intersection common to both sets.

What is the difference between intersection and union. The meaning is different. And is the meaning of addition, and the set of all the elements of two sets is the union of two sets.

Intersect means public, and the set of common elements in two sets is the intersection of two sets.

Represents different. Union, a set with elements belonging to a or belonging to b as elements is called the union of a and b, denoted a b or b a, and is pronounced "a and b" or "b and a".

The nature is different. A union is a set of two or more elements that are duplicated and only one is taken, and an intersection is a set of elements common to two or more sets.

Learn how to intersect and union

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There is no only way to do math problems, as long as it is logical and reasonable, and you can deduce the conclusion step by step, you don't have to stick to the method taught by the teacher. You can also use drawing, test value method, substitution method, etc. to do math problems, as long as you concentrate on research, hard work pays off, and mathematics can always be learned well.

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.

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.

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.

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.

1. The nature is not bai

Same: In general, for a given DU of two sets.

The intersection of zhia and set b is dao refers to the inclusion of all elements that belong to both a and b, and in other branches of set theory, 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={x丨x a and x b}; A and b are juxtaposed to write "a b", i.e. a b=.

The intersection is represented by "bai", which is the du of both

For example, a={dao1,2,3,4},b={回3,4,5,6}, then the intersection of ab is a b={3,4}

The union is denoted by " ", A.

The union is all the elements of both, as in the example above, then the union of ab, i.e. a b={1,2,3,4,5,6} Note that there can be no duplicate elements in the set.

Union refers to a set of all the elements in two sets.

An intersection is a set that coincides in two sets.