"Basic Relationships of Sets" Sets and Common Logic Terms PPT Courseware

Description

"Basic Relationships of Sets" Sets and Common Logic Terms PPT Courseware

Part One: Learning Objectives

Understand the concepts of subsets and proper subsets, and be able to use enumeration methods to find all subsets of finite sets

Can use symbols and Venn diagrams to express the relationship between sets, and can judge the relationship between two sets

Able to solve simple parameter-seeking problems based on the relationship between sets

Basic relations of sets PPT, part 2 content: independent learning

Problem guide

Preview textbooks P9-P13 and think about the following questions:

1. What are the relationships between sets and sets? How can these relationships be represented symbolically?

2. What is a subset of a set? What is a true subset? How to express it symbolically?

3. What is the concept of set equality?

A preliminary exploration of new knowledge

1. Subset

(1) Concept: Generally, if any element of set A is an element of set B, then set A is called a subset of set B.

(2) Notation: A⊆B (or B⊇A)

(3) Reading: A is included in B (or "B includes A")

(4) If A is not a subset of B, it is recorded as A⊆/B (or B⊉A) and read as "A does not include B" (or "B does not include A").

(5) Properties: A⊆A; ∅⊆A.

2. True subset

(1) Concept: Generally, if set A is a subset of set B, and at least one element in B does not belong to A, then set A is called a proper subset of set B.

(2) Notation: A�B (or B�A)

(3) Reading: A really includes B (or "B really includes A")

(4) Properties: For the set A, B, C, ① if A⊆B, B⊆C, then A_____C; ② if A�B, B�C, then A_____C.

3. Venn diagram

If a set is represented by a closed curve on a plane, this diagram is usually called a Venn diagram.

4. The relationship between equality and subsets of sets

(1) Generally speaking, if the elements of set A and set B ____________, then set A and set B are said to be equal, denoted as _________, and pronounced as "A equals B".

(2) From the equality of sets and the definition of subsets, it can be seen that if ________ and ________, then A = B; conversely, if A = B, then ________ and ________.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) "∈" and "⊆" have the same meaning. ()

(2) The empty set is a proper subset of any set. ()

(3) If set A is a proper subset of set B, then there must be elements in set B that are not in set A. ()

(4) If a∈A, set A is a subset of set B, then there must be a∈B.()

(5) {1, 2, 3} = {3, 2, 1}. ()

It is known that the set M={1}, N={1, 2, 3}, the relationship between the set M and N can be accurately represented by ()

A． M

C． N⊆M D. M�N

It is known that the set A={x|x is a triangle}, B={x|x is an isosceles triangle}, C={x|x is an isosceles right triangle}, D={x| ;x is an equilateral triangle}, then ()

A． A⊆B B. C⊆B

C． D⊆C D． A⊆D

It is known that the set A = {0, 1}, B = {-1, 0, a + 3}, and A⊆B, then a = ________.

PPT on the basic relationship of sets, the third part: lecture and interaction

Judgment of relationships between sets

Indicate the relationship between the following pairs of sets:

(1)A={-1,1}, B={(-1,-1), (-1,1), (1,-1), (1,1)};

(2)A=(-1,4), B=(-∞,5);

(3) A={x|x is an equilateral triangle}, B={x|x is an isosceles triangle};

(4)M={x|x=2n-1, n∈N*}, N={x|x=2n+1, n∈N*}.

Track training

1. The Venn diagram that can correctly represent the relationship between the set M={x∈R|0≤x≤2} and the set N={x∈R|x2-x=0} is ()

2. It is known that the set A={x|x2-3x+2=0}, B={1, 2}, C={x|x<8, x∈N}, fill in the blanks with appropriate symbols:

(1)A________B; (2)A________C;

(3){2}________C; (4)2________C.

Questions about the number of subsets and proper subsets

(1) (2019•Anqing Testing) It is known that the set A={x∈R|x2-3x+2=0}, B={x∈N|0

A． 1B. 2

C． 3D． 4

(2) It is known that the set A = {x∈R|x2=a}, so that the value of a when the number of subsets of the set A is 2 is ()

A． -2 B. 4

C． 0D. The answer is none of the above

(3) If the set A = {2, 3, 4}, B = {x|x=mn, m, n∈A and m≠n}, then the number of non-empty proper subsets of the set B is ( )

A． 3B． 6

C． 7D. 8

regular method

(1) Three steps to find the number of subsets and proper subsets of a set

(2) Four conclusions related to the number of subsets and proper subsets

Suppose the set A contains n elements, then we have

①The number of subsets of A is 2n;

②The number of non-empty subsets of A is 2n-1;

③The number of proper subsets of A is 2n-1;

④The number of non-empty proper subsets of A is 2n-2.

Sets are equal

(1) Given the following 5 sets:

①M＝{(-5,3)}, N＝{-5,3};

②M＝{1,-3}, N＝{3,-1};

③M＝∅，N＝{0};

④M={π}, N={3.141 5};

⑤M={x|x2-3x+2=0}, N={y|y2-3y+2=0}.

Among them are equal sets ()

A． 1 group B. 2 teams

C． 3 groups D. 4 groups

regular method

(1) Whether two sets are equal cannot only be judged from the form of the sets. All elements of the two sets should be determined first, and then judged according to the definition of set equality.

(2) To find coefficients based on set equality, we should start from the concept of set equality and find the relationship between the elements in the two sets. First, analyze which element in one set is equal to which element in another set. There are several situations, and then solve it through a series of equations (set). When there is more than one unknown element in the set, it is often necessary to classify and discuss it. After obtaining the parameter values, pay attention to check whether the mutuality of the elements in the set is satisfied.

Basic relationship between sets PPT, Part 4: Feedback on compliance with standards

1. It is known that the set A={x|x=3k, k∈Z}, B={x|x=6k, k∈Z}, then the most suitable relationship between A and B is ()

A． A⊆B　B. A⊇B

C． A�B D. A�B

2. The set M satisfying {a}⊆M�{a, b, c, d} has a total of ()

A． 6 B． 7

C． 8 D. 15

3. Suppose the set A={x, y}, B={0, x2}, if A=B, then the value of real number x is ________, and the value of y is ________.

4. Assume the set A = {1, 3, a}, B = {1, 1-2a}, and B ⊆ A, then the value of a is ________.

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Update Time: 2024-10-20

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