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

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

Part One: Learning Objectives

Understand the concepts of subsets, proper subsets, and empty sets, 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 relationships between sets PPT, part 2: independent learning

Problem guide

Preview textbook P7-P8 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 kind of set is the empty set? What is the relationship between the empty set and other sets?

A preliminary exploration of new knowledge

1. Venn diagram

(1) Definition: In mathematics, we often use ______ of a closed curve on a plane to represent a set. This kind of diagram is called a Venn diagram. This method of representing a set is called graphical representation.

(2) Scope of application: Sets with a small number of elements.

(3) How to use: Write the elements inside the closed curve.

■Instructions from famous teachers

The boundary of the Venn diagram representing a set is a closed curve, which can be a circle, rectangle, ellipse, or other closed curve.

2. concept of subset

written language

Generally speaking, for two sets A and B, if the ____________ elements in set A are all elements of set B, set A is called a subset of set B.

Symbolic language A______B(or B⊇A)

graphic language

■Instructions from famous teachers

"Set A is a subset of set B" can be expressed as: if x∈A, then x∈B.

3. The concept of set equality

Generally speaking, if the ____________________ of set A are all elements of set B, and the ____________________ of set B are all elements of set A, then set A and set B are equal, denoted as ______, that is to say, if _ _____, and ______, then A=B.

4. The concept of proper subset

■Instructions from famous teachers

(1) If A⊆B, and B⊆A, then A=B; conversely, if A=B, then A⊆B, and B⊆A.

(2) If two sets are equal, the elements contained in the two sets are exactly the same, regardless of the order in which the elements are arranged.

(3) In the definition of a proper subset, A�B must first satisfy A⊆B, and secondly, there must be at least one x∈B, but x∉A.

5. empty set

(1) Definition: The set of ____________________ is called the empty set.

(2) Symbolally expressed as: ______.

(3) Provision: The empty set is ______ of any set.

6. Relevant properties of subsets

(1) Any set is its own ______, that is, A______A.

(2) For the set A, B, C, if A⊆B, and B⊆C, then ______.

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 set {0} is the empty set. ()

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

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

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

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

PPT on the basic relationship between sets, the third part: lecture, practice 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＝{x|-1

(3) A={x|x is a square}, B={x|x is a rectangle};

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

[Solution] (1) The representative elements of set A are numbers, and the representative elements of set B are ordered pairs of real numbers, so there is no inclusive relationship between A and B.

(2) Set B = {x|x<5}, use number axes to represent sets A and B, as shown in the figure, and it can be seen from the figure that A�B.

(3) A square is a special rectangle, so A�B.

(4) Both sets represent sets of positive odd numbers, but since n∈N*, the set M contains the element “1”, while the set N does not contain the element “1”, so N�M.

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 ()

Analysis: Option B. Solve x2-x=0 to get x=1 or x=0, so N={0, 1}, it is easy to get N�M, and the corresponding Venn diagram is shown in option B.

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.

Analysis: Set A is the solution set of equation x2-3x+2=0, that is, A={1, 2}, and C={x|x<8, x∈N}={0, 1, 2, 3, 4, 5, 6, 7}. Therefore (1)A=B; (2)A�C; (3){2}�C; (4)2∈C.

PPT on the basic relationship between sets, part 4: feedback on compliance with standards

1. Which of the following propositions is correct ()

A． The empty set has no subsets

B． The empty set is a proper subset of any set

C. Any set must have two or more subsets

D. Suppose the set B⊆A, then if x∉A, then x∉B

Analysis: Choose D. The empty set has only one subset, which is itself, so A and C are wrong; the empty set is a proper subset of any non-empty set, so B is wrong; from the concept of subset, we know that D is correct.

2. 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

Analysis: Choose D. Set A is a set of integers divisible by 3, and set B is a set of integers divisible by 6, so B�A.

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

A． 6 B. 7

C. 8 D. 15

Analysis: Choose B. According to the meaning of the question, a∈M, and M�{a, b, c, d}, so M must contain element a, and can contain 0, 1 or 0 of elements b, c, d. 2, that is, the number of M is equal to the number of proper subsets of the set {b, c, d}, there are 23-1=7 (pieces).

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