"Sets and Their Representation Methods" Sets and Common Logic Terms PPT Courseware (The Meaning of Sets in Lesson 1)

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"Sets and Their Representation Methods" Sets and Common Logic Terms PPT Courseware (The Meaning of Sets in Lesson 1)

Part One: Learning Objectives

1. Understand the meaning of sets through examples. (difficulty)

2. Master the three characteristics of elements in a set. (emphasis)

3. Understand the "belonging" relationship between elements and sets, remember the commonly used symbols for number sets and be able to apply them. (Key point, easy to confuse)

core competencies

1. Gradually develop mathematical abstract literacy through the learning of collective concepts.

2. Cultivate logical reasoning skills through the application of the mutuality of elements in a set.

Sets and their representation methods PPT, part 2: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

1. Concepts related to elements and sets

(1) Set: When some determinable and different ______ are brought together, it is said that these objects form a set (sometimes referred to as a set), which is often represented by English capital letters ______________.

(2) Element: Each ______ that makes up a set is an element of this set, often represented by English lowercase letters ______.

(3) Sets are equal: Given two sets A and B, if the elements that make up them are completely ________, the two sets are said to be equal, recorded as A=B.

(4) Characteristics of elements in the set: _______, _______ and _______.

Thinking: (1) Can all the "handsome guys" in a certain class form a set?

(2) Can boys in a certain class whose height is higher than 175 cm form a group?

Tips: (1) All the "handsome guys" in a certain class cannot form a set, because there is no clear standard for "handsome guys".

(2) Boys in a certain class whose height is higher than 175 cm can form a set because the standard is determined.

2. The relationship between elements and collections

(1) Belongs to: If a is an element of set A, it is said to be _______, recorded as ________.

(2) Does not belong: If a is not an element in set A, it is said that _______ is recorded as _______.

3. empty set

We call a set that does not contain any elements an empty set, denoted as ______.

First try

1. Among the objects given below, which one can form a set is ()

A． All big numbers

B. Good Samaritan

C． beautiful little girl

D. All students admitted to Tsinghua University in 2019

2. The number of elements in the set formed by the letters in "book" is ()

A． 1B. 2C. 3D. 4

3. Use "∈" or "∉" to fill in the blanks:

12________N; -3________Z; 2________Q; 0________N*; 5________R.

4. It is known that the set M has two elements 3 and a+1, and 4∈M, then the real number a=________.

Sets and their representation methods PPT, the third part of the content: cooperative exploration to improve literacy

Basic concepts of collections

[Example 1] Examine each of the following groups of objects. Which one can form a set is ()

①The most beautiful countryside across China;

②The point with equal horizontal and vertical coordinates in the Cartesian coordinate system;

③A natural number not less than 3;

④The gold medal winner of the 23rd Winter Olympics in 2018.

A． ③④　B. ②③④

C． ②③ D. ②④

regular method

Criteria for judging whether a group of objects can form a set

To judge whether a group of objects can form a set, the key is to see whether the group of objects satisfies certainty. If the group of objects satisfies the certainty, it can form a set; otherwise, it cannot form a set. At the same time, we must also pay attention to the mutuality and independence of the elements in the set. Sequence.

Track training

1. Decide whether the following statements are correct and explain why.

(1) All natural numbers greater than 3 and less than 5 form a set;

(2) Some points in the first quadrant of the Cartesian coordinate plane form a set;

(3) The set of all solutions to equation (x-1)2(x+2)=0 has 3 elements.

[Solution](1) is correct. The elements in (1) are definite and different from each other, and can form a set.

(2) is incorrect. The standard of "some points" is not clear and cannot form a set.

(3) is incorrect. The solutions to the equation are only 1 and -2, and there are 2 elements in the set.

The relationship between elements and collections

[Example 2] (1) The correct number of the following relationships is ()

①π∈R; ②2∉Q; ③0∈N*; ④|-5|∉N*.

A． 1B． 2C． 3D. 4

(2) It is known that set A contains three elements 2, 4, 6, and when a∈A, there is 6-a∈A, then a is ()

A． 2B. 2 or 4

C． 4 D. 0

regular method

Two methods to determine the relationship between elements and sets

1 Direct method: If the elements in the set are given directly, just judge whether the element appears in the known set.

2 Reasoning method: For some sets that are not directly represented, it is only necessary to determine whether the element satisfies the characteristics of the elements in the set. At this time, it should first be clear what characteristics the elements in the set have.

Characteristics and applications of elements in collections

[Inquiry Questions]

1. If set A contains two elements a and b, what relationship does a and b satisfy?

Hint: a≠b.

2. If 1∈A, what is the relationship between element 1 and elements a and b in set A?

Tip: a=1 or b=1.

regular method

1. To solve problems containing letters, the idea of ​​classification discussion is often used. When conducting classification discussion, the classification standards must be clear.

2. In this question, after solving the equation to find the value of a, we often forget to verify the mutuality of the elements in the set, resulting in procedural points loss.

Reminder: When answering such questions, it is easy to ignore the mutuality and lead to root increase.

Class summary

1. The basis for judging whether the entire set of objects can form a set is the certainty of the elements. If the object under examination is certain, the set can be formed, otherwise it cannot be formed.

2. The elements in the set have three characteristics. When solving for the letter parameter value (range) related to the set, it is necessary to use the mutuality of the elements in the set to check whether the required parameters meet the requirements.

3. When answering questions about the relationship between elements containing letters and sets, you must have the awareness of classification and discussion.

Sets and their representation methods PPT, the fourth part: reaching the standard in class and solidifying the double base

1. Thinking and analysis

(1) Numbers close to 0 can form a set. ()

(2) The two sets consisting of elements 0,1,2 and 2,0,1 respectively are equal. ()

(3) Two identical elements can be found in a set. ()

2. It is known that the set A consists of numbers x<1, then there is ()

A． 3∈A B. 1∈A

C． 0∈A D. -1∉A

3. Which of the following groups of objects cannot form a set ()

A． nonnegative real numbers up to 20

B. Solution of equation x2-9=0 in the range of real numbers

C. All approximations of √3

D. All students in a certain school who are over 170cm tall

4. It is known that set A contains two elements a-3 and 2a-1. If -3∈A, try to find the value of real number a.

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Update Time: 2024-11-26

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