A set of certain, definite and distinguishable things is regarded as a whole, which is called a set for short, and each thing is called an element or a yuan for short. Such as (1) the different Chinese characters appearing in the true story of Ah Q (2) the classification of all English capital letters:
Union: The set whose elements belong to A or B is called the union (set) of A and B, and it is recorded as A? B (or b? A), pronounced -a and B‖ (or -b and A‖), that is, a? B={x|x？ A, or x B} intersection: The set with elements belonging to A and B as elements is called the intersection (set) of A and B, and recorded as A? B (or b? A), pronounced -A to B‖ (or -B to A‖), that is, a? B={x|x？ A and x? B}
Difference: The set of elements belonging to A but not to B is called the difference between A and B (set).
Note: An empty set is contained in any set, but it cannot be said that it belongs to any set.
Note: An empty set belongs to any set, but not to any element.
When some specified objects are set together, they become a set. Finite sets contain finite elements, infinite sets contain infinite elements, and empty sets contain no elements. Remember? .
The nature of the set:
Determinism: Every object can determine whether it is an element of a set. Without certainty, there will be no trap. For example, a tall classmate and a small one cannot form a set.
Correlation: Any two elements in a collection are different objects. It cannot be written as {1, 1, 2}, but as {1, 2}. Disorder: {a, b, c}{c, b, a} are the same set.
A set has the following properties: If A is contained in B, then A? B=A，A？ B=B
Symbols of commonly used number sets:
(1) The set of all non-negative integers is usually called the set of non-negative integers (or the set of natural numbers), and is recorded as n.
(2) Exclude the set of 0 from the set of non-negative integers, also known as the set of positive integers, and record it as N+ (or N*).
(3) The set of all integers is usually called the set of integers, and is denoted as z..
(4) The set of all rational numbers is usually referred to as the rational number set for short, and is recorded as Q..
(5) The set of all real numbers is usually called the set of real numbers, and the stage is r.
Operation of sets:
1. commutative law
Answer? B=B？ A
Answer? B=B？ A
2. Association law
(A？ b)？ C=A？ (B？ c)
(A？ b)？ C=A？ (B？ c)
3. Distribution law
Answer? (B？ C)=(A？ b)？ (A？ c)
Answer? (B？ C)=(A？ b)？ (A？ c)
One set of compulsory mathematics for senior one of Beijing Normal University 1. The known sets A={a2, a+ 1, -3}, B={a-3, 2a- 1, A2+ 1}, a? B = {-3}, find the value of a.
∵ A？ B={-3}
? -3? B.
① if a-3=-3, then a=0, then a = {0, 1, -3}, B={-3,-1, 1}
? Answer? B = {-3, 1} and? B = {-3} is contradictory, so a-3? -3.
② If 2a- 1=-3, then a=- 1, then a = {1, 0,3}, and b = {-4,3,2}.
At this time, one? B = {-3} meets the problem, so a=- 1.
2. Among the following four sets, the difference from the other three sets is ().
A.{y|y=2} B.{x=2}
C.{2} D.{x|x2-4x+4=0}
Analysis {x=2} represents a set of equations, so B.
3. In the following relationship, the correct number is _ _ _ _ _ _ _ _.
① 12? r； ② 2? q； ③|-3|? n *； ④| -3|? Ask.
Analyze this problem to investigate the relationship between commonly used number sets and elements and sets. Mingming 12? R, ① correct; 2? Q, ② Correct;
|-3|=3? N*，|-3|=3？ Q, ③ and ④ are incorrect.
Answer 2
4. Given sets A={ 1, x, x2-x} and B={ 1, 2, x}, if set A is equal to set B, find the value of x. 。
Analysis because set a is equal to set b,
So x2-x=2. X=2 or x=- 1.
When x=2, it contradicts the anisotropy of set elements.
When x=- 1, it meets the meaning of the question.
? x=- 1。
Beijing normal university printing plate high school mathematics compulsory exercise 1. The correct one of the following propositions is ()
①0 and {0} represent the same set; ② The set composed of 1, 2,3 can be expressed as {1, 2,3} or {3,2,1}; ③ The set of all solutions of equation (x- 1)2(x-2)=0 can be expressed as {1, 1, 2}; ④ Setting {x|4
A. Only ① and ④ B. Only ② and ③
C. Only ② D. None of the above statements are correct.
Parsing {0} means that the element is a set of 0, and 0 only means one element, so ① error; ② It is correct to conform to the disorder of elements in the set; ③ dissimilarity and error of elements in inconsistent sets; (4) There are infinite elements in C, which cannot be enumerated one by one, so it cannot be expressed by enumeration.
Answer c
2. Enumeration indicates that the set {x|x2-2x+ 1=0} is ().
A.{ 1， 1} B.{ 1}
C.{x= 1} D.{x2-2x+ 1=0}
The analytic set {x|x2-2x+ 1=0} is essentially the solution set of equation x2-2x+ 1=0. This equation has two equal real roots which are 1, so it can be expressed as {1}.
Answer b
3. known set A={x? N*|-5？ x？ 5}, there will be ()
A.- 1? A B.0? A
C.3？ A D. 1? A
Analysis ∵x? N*，-5？ x？ 5,
? x= 1，2，
That is A={ 1, 2}, 1? A. therefore, choose D.
Answer d
4. Define set operation: A*B={z|z=xy, x? a，y？ B}。 Let A={ 1, 2} and B={0, 2}, then the sum of all elements of set A*B is ().
A.0 B.2
C.3 D.6
According to the meaning of the question, A * B = {0,2,4}, and the sum of all its elements is 6, so D is chosen.