"Basic Operations of Sets" Sets and Common Logic Terms PPT Download (Complete Collection, Supplement and Comprehensive Application of Lesson 2)

Description

"Basic Operations of Sets" Sets and Common Logic Terms PPT Download (Complete Collection, Supplement and Comprehensive Application of Lesson 2)

Part One: Learning Objectives

1. Understand the meaning of the complete set and its symbolic representation. (easy to mix)

2. Understand the meaning of the complement of a subset in a given set, and be able to find the complement of a given subset. (main difficulty)

3. Can use Venn diagrams and number lines to perform set operations. (emphasis)

core competencies

1. Cultivate mathematical operation literacy through the operation of complement sets.

2. Use collective thinking to judge and classify objects in real life and cultivate mathematical abstract literacy.

Basic operations on sets PPT, part 2: independent preview

1. Complete works

(1) Definition: If a set contains _____ involved in the problem under study, then the set is called a complete set.

(2) Notation: The complete set is usually notated as .

Thinking: Does the complete set have to be the set R of real numbers?

Tip: The universal set is a relative concept that changes due to different research problems. For example, when solving inequalities in the range of real numbers, the universal set is the set of real numbers R, and when solving inequalities in the range of integers, the universal set is the set of integers Z.

2. Complement

Literal language For a set A, the set consisting of all elements of _____________ in the complete set U is called the complement of the set A relative to the complete set U, and is denoted as ____

Symbolic language ∁UA＝______________

First try

1. It is known that the complete set U={0,1,2}, and ∁UA={2}, then A=()

A． {0}B． {1}

C． ∅D． {0,1}

2. Suppose the complete set is U, M={0,2,4}, ∁UM={6}, then U is equal to ()

A． {0,2,4,6} B. {0,2,4}

C． {6} D. ∅

3. If the set A={x|x>1}, then ∁RA=________.

Basic operations of sets PPT, the third part: cooperative exploration to improve literacy

Complement operation

[Example 1] (1) It is known that the complete set is U, the set A={1,3,5,7}, ∁UA={2,4,6}, ∁UB={1,4,6}, then the set B=________;

(2) It is known that the complete set U={x|x≤5} and the set A={x|-3≤x<5}, then ∁UA=________.

(1){2,3,5,7}　(2){x|x<-3 or x=5}　(1) Method 1 (Definition method): Because A={1,3 ,5,7}, ∁UA={2,4,6}, so U={1,2,3,4,5,6,7}.

And ∁UB={1,4,6},

So B={2,3,5,7}.

regular method

How to find the complement of a set

1. Definition method: When there are few elements in the set, the definition can be used to solve directly.

2Venn diagram method: With the help of Venn diagram, the complete set and complement can be found intuitively.

3 Number axis method: When the elements in the set are continuous and infinite, you can use the number axis to solve the problem. At this time, you need to pay attention to the endpoint problem.

Track training

1. (1) Suppose the set A={x∈N*|x≤6}, B={2,4}, then ∁AB is equal to ()

A． {2,4}B． {0,1,3,5}

C． {1,3,5,6} D. {x∈N*|x≤6}

(2) It is known that U={x|x>0}, A={x|2≤x<6}, then ∁UA=______.

Comprehensive operations of set intersection, union and complement

[Example 2] Let the complete set be R, A={x|3≤x<7}, B={x|2

Techniques for solving set intersection, union and complement operations

1. If the given set is a finite set, first list the elements in the set one by one, and then solve it by combining the definitions of intersection, union, and complement. In the solution process, Venn diagram is often used to solve the problem.

2. If the given set is an infinite set, you often use the number axis to express the known set and the complete set on the number axis respectively, and then perform the operations of intersection, union, and complement. Pay attention to boundary issues during the solution process.

Solving parameter values ​​related to complement set

[Inquiry Questions]

1. If A and B are subsets of the complete set U, and (∁UA)∩B=∅, what is the relationship between sets A and B?

Hint: B⊆A.

2. If A and B are subsets of the complete set U, and (∁UA)∪B=U, what is the relationship between the sets A and B?

Hint: A⊆B.

regular method

Method of solving parameters from the complement of sets

1. If the given set is a finite set, when determining the parameter problem from the complement set, the complement set definition can be used and combined with knowledge to solve the problem.

2. If the given set is an infinite set, parameter-finding problems related to set intersection, union, and complement operations are generally solved using the number line analysis method.

Class summary

1. The prerequisite for finding the complement of a certain set must be clear about the complete set. The complements of the same set under different complete sets are different.

2. Complementary set, as a way of thinking, has opened up new ideas for us to study problems. When forward thinking is blocked, we can use reverse thinking. If it is difficult to directly find A, we can use the "directly find the opposite if it is difficult" strategy, first find ∁UA, Then find A from ∁U(∁UA)=A.

Basic operations of sets PPT, part 4: reaching the standard and solidifying the double base in class

1. Thinking and analysis

(1) The complete set must contain any elements. ()

(2) Set ∁RA = ∁QA.()

(3) The complement of a set must contain elements. ()

2. U={0,1,2,3,4}, set A={1,2,3}, B={2,4}, then (∁UA)∪B is ()

A． {1,2,4}B. {2,3,4}

C． {0,2,3,4} D． {0,2,4}

3. Suppose the set S={x|x>-2}, T={x|-4≤x≤1}, then (∁RS)∪T is equal to ()

A． {x|－2

C． {x|x≤1} D. {x|x≥1}

4. It is known that the complete set U={2,0,3-a2}, the subset of U={2, a2-a-2}, ∁UP={-1}, find the value of the real number a.

Keywords: Free download of the compulsory course I PPT courseware of high school PEP B version of mathematics, PPT download of basic operations on sets, PPT download of sets and commonly used logical terms, PPT download of complete sets, supplements and comprehensive applications, .PPT format;

For more information about the PPT courseware "Sets and Commonly Used Logical Terms: The Complete Set of Basic Operations and Their Comprehensive Application" PPT courseware, please click on the "Sets and Commonly Used Logic Terms: Basic Operations of Sets ppt Complete Set and Complement and Comprehensive Application" ppt tag.

"End of Chapter Review Course" collection and common logic terms PPT courseware:

"End of Chapter Review Course" Sets and Common Logic Terms PPT Courseware Question Type Explores the Union, Intersection, and Complement Operations of Sets [Example 1] It is known that the complete set U={0,1,2,3,4,5,6}, the set A={xN|1

"End-of-Chapter Review and Improvement Course" collection and common logic terms PPT:

"End-of-Chapter Review and Improvement Course" Sets and Common Logic Terms PPT Part One: Comprehensive Improvement of Basic Concepts of Sets (1) It is known that set A = {0, 1, 2}, then set B = {x-y| The number of elements in xA, yA} is ( ) A. 1B. 3C. 5 D. 9 (2)If-..

"Sufficient conditions, necessary conditions" collection and common logical terms PPT (sufficient and necessary conditions in lesson 2):

"Sufficient and Necessary Conditions" collection and common logical terms PPT (Lesson 2: Necessary and Sufficient Conditions) Part One Content: Learning Objectives 1. Understand the concept of necessary and sufficient conditions. (Difficulty) 2. Ability to determine the sufficiency, necessity, and sufficiency of conditions. (Key points) 3. Will proceed...

File Info

Update Time: 2024-11-19

This template belongs to Mathematics courseware People's Education High School Mathematics Edition B Compulsory Course 1 industry PPT template

Preview