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

Description

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

Part One: Learning Objectives

Understand the concepts of sets and elements

Understand the relationship between elements and sets, and master some common sets and their notations in mathematics

Understand the characteristics of elements in a set and be able to use them to solve problems

Sets and their representation methods PPT, part 2: independent learning

Problem guide

Preview the contents of textbook P3-P5 and think about the following questions:

1. What are the concepts of sets and elements?

2. How to represent sets and elements using letters?

3. What are the two relationships between elements and sets?

4. What are the common number sets? What symbols are used to represent them?

5. According to the number of elements, what categories can sets be divided into?

A preliminary exploration of new knowledge

1. The concept of elements and sets

(1) Set: Considering some objects that can __________ and __________ as a whole, it is said that the whole is a set composed of these objects (sometimes referred to as a set), usually represented by English capital letters A, B, C,... ．

(2) Elements: The _____________ that make up a set are all elements of this set, usually represented by English lowercase letters a, b, c,...

(3) Characteristics of elements

①Deterministic: The elements of the set must be __________;

② Mutuality: For a given set, the elements in the set must be __________.

③Disorder: The elements in the set can be arranged arbitrarily, regardless of order.

■Instructions from famous teachers

(1) When solving a set problem, you must first clarify what the elements in the set are. The elements in the set can be points, or some people or some objects.

(2) The order of the elements in the set has nothing to do with it. As long as the elements in the two sets are the same, the two sets are the same set.

2. The relationship between elements and collections

■Instructions from famous teachers

Two points on the relationship between elements and sets

(1) The symbols "∈" and "∉" describe the relationship between elements and sets. For an element a and a set A, there are only two results: "a∈A" and "a∉A".

(2) "∈" and "∉" are directional, with elements on the left and sets on the right. The form "R∈0" is wrong.

3. empty set

(1)Definition: The set of _______________.

(2)Symbol:______．

4. Commonly used number sets and their notation

5. Classification of collections

(1) Sets Finite set: a set containing ________ elements Infinite set: a set containing ________ elements

(2) The empty set is a ________ set.

self-test

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

(1) The elements in the set must be numbers. ()

(2) All the students in Grade 1 and Grade 4 form a group. ()

(3) The set consisting of 1, 2, 3 and the set consisting of 3, 2, 1 are the same set. ()

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

(5)The smallest element in the set N is 0.()

(6) If a∈Q, then there must be a∈R.()

The number of elements in the set composed of letters in "title" is ()

A． 2B． 3

C． 4 D. 5

Among the following relationships: ①0.21∈Q; ②105∉N*; ③-4∈N*; ④4∈N; ⑤0∈∅. The correct number is ()

A． 0 b． 1

C． 2 D. 3

Sets and their representation PPT, the third part: lecture and interaction

collection concept

In September 2019, we entered the campus of our favorite high school and found our class. Which of the following objects can form a set? And explain your reasons.

(1) All classmates in your class;

(2) Students who are higher in the class;

(3) Students in the class who are over 178 cm tall;

(4) The fatter students in the class;

(5) Students in the class who weigh more than 75 kg;

(6) Students with better academic performance.

[Answer] (1) All the students in the class are certain, so they can form a set.

(2) Because "relatively high" cannot be measured, the object is uncertain, so it cannot form a set.

(3) Because "height exceeds 178 cm" is certain, it can form a set.

(4) Because "fatter" cannot be measured, the object is uncertain, so it cannot form a set.

(5) Because "weight exceeds 75 kg" is certain and can form a set.

(6) Because "better academic performance" cannot be measured, the object is uncertain, so it cannot form a set.

regular method

Method to determine whether a set of objects can form a set

Generally, the process of confirming whether a set of objects a1, a2, a3,...,an (a1, a2,...,an are all different) can form a set is

The relationship between elements and collections

(1) Among the following relationships, the correct one is ()

①12∈R; ②2∉Q; ③|-3|∈N; ④|-3|∈Q.

A． 1 B． 2

C． 3 D. 4

(2) Satisfying "a∈A and 4-a∈A, a∈N and 4-a∈N", the number of sets A with only 2 elements is ()

A． 0 b. 1

C． 2 D． 3

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 is given in the known set. At this time, you should first clarify which elements the set is composed of.

(2) Inference method: For some sets that are inconvenient to express directly, when judging the relationship between an element and the set, you only need to judge whether the element satisfies the characteristics of the elements in the set. At this time, we should first clarify what attributes the elements of the known set have, that is, what expressions or conditions the elements in the set should meet.

Characteristics and applications of elements in collections

It is known that the set A contains two elements a and a2. If 1∈A, the value of the real number a is ________.

Interactive exploration

1. (Variable condition) If the condition "1∈A" in this example is removed, what is the value range of the real number a?

2. (Variable conditions) If "1∈A" in this example is changed to "2∈A", what is the value of a?

3. (Variable condition) If the set consisting of a and a2 has only one element, what is the value of a?

Sets and their representation methods PPT, Part 4: Feedback on compliance with standards

1. The following groups of objects can form a set ()

A． All difficult questions in Mathematics Compulsory Course 1 textbook

B. All prime numbers less than 8

C． Some points in the first quadrant of the Cartesian coordinate plane

D. all small positive numbers

2. Among the following conclusions, which one is incorrect ()

A． If a∈N, then 1a∉N

B. If a∈Z, then a2∈Z

C． If a∈Q, then |a|∈Q

D. If a∈R, then 3a∈R

3. If the solutions to the equations x2-5x+6=0 and x2-x-2=0 are used as elements to form a set M, then the number of elements in M ​​is ()

A． 1B. 2

C． 3D． 4

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Update Time: 2024-09-29

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