"Basic Operations of Sets" Sets and Common Logic Terms PPT Courseware (Lesson 1 Union and Intersection)

Description

"Basic Operations of Sets" Sets and Common Logic Terms PPT Courseware (Lesson 1 Union and Intersection)

Part One: Learning Objectives

1. Understand the meaning of the union and intersection of two sets, and be able to find the union and intersection of two simple sets. (main difficulty)

2. Be able to use Venn diagrams to express the relationships and operations of sets, and appreciate the role of diagrams in understanding abstract concepts. (difficulty)

core competencies

1. Use Venn diagrams to cultivate intuitive imagination literacy.

2. Improve mathematical operation literacy through the operations of set union and intersection.

Basic operations on sets PPT, part 2: independent preview to explore new knowledge

A preliminary exploration of new knowledge

1. Union

Thinking: (1) What kind of situations does "x∈A or x∈B" include?

(2) Is the number of elements in set A∪B equal to the sum of the number of elements in set A and set B?

Tips: (1) The condition "x∈A or x∈B" includes the following three situations: x∈A, but x∉B; x∈B, but x∉A; x∈A, and x∈B. Use Venn diagram to represent it as shown in the figure.

(2) Not equal, the number of elements of A∪B is less than or equal to the sum of the number of elements of set A and set B.

2. intersection

3. Operational properties of union and intersection

First try

1. Assume the set M={-1,0,1}, N={0,1,2}, then M∪N=________, M∩N=________.

2. If the set A={x|-32}, then A∪B=________.

3. The set B satisfying {1}∪B={1,2} may be equal to ________.

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

Union concept and its application

[Example 1] (1) Suppose the set M={x|x2+2x=0, x∈R}, N={x|x2-2x=0, x∈R}, then M∪N=()

A． {0} B. {0,2}

C. {-2,0} D. {-2,0,2}

(2) It is known that the set M={x|-35}, then M∪N=()

A． {x|x<-5 or x>-3} B. {x|－5

C. {x|－35}

(1)D　(2)A　M＝{x　x2＋2x＝0，x∈R}＝{0，-2}，N＝{x　x2－2x＝0，x∈ R}={0,2}, so M∪N={-2,0,2}, so choose D.

(2) Express the set M, N on the number axis, as shown in the figure, then M∪N={x|x<-5 or x>-3}.

regular method

Two basic methods for finding the union of sets

1Definition method: If the set is expressed by enumeration method, it can be solved directly by using the definition of union;

2Number-shape combination method: If the set is a number set composed of real numbers represented by the descriptive method, it can be solved with the help of the number line analysis method.

Intersection concepts and their applications

[Example 2] (1) Suppose the set A={x|-1≤x≤2}, B={x|0≤x≤4}, then A∩B is equal to ()

A． {x|0≤x≤2}B． {x|1≤x≤2}

C. {x|0≤x≤4} D． {x|1≤x≤4}

(2) It is known that the set A={x|x=3n+2, n∈N}, B={6,8,10,12,14}, then the number of elements in the set A∩B is ()

A． 5B． 4C. 3D． 2

regular method

1. The operation of finding the intersection of sets is similar to the operation of union. The method is:

(1) Definition method, (2) Number-shape combination method.

2. If A and B are infinite continuous number sets, the number axis is often used to solve the problem. But it should be noted that when expressing inequalities using a number line, values ​​containing endpoints are represented by real points, and values ​​without endpoints are represented by hollow points.

Class summary

1. Understanding of the concepts of union and intersection

(1) For unions, we should pay attention to the meaning of "or". There is a principled difference between "or" and the commonly said "either-or". They are "compatible". The condition "x∈A, or x∈B" includes the following three situations: x∈A but x∉B; x∈B but x∉A; x∈A and x∈B. Therefore, A∪B is A set consisting of all elements belonging to at least one of A and B.

(2) The elements in A∩B are "all" elements that belong to set A and belong to set B, not some. In particular, when set A and set B have no common elements, it cannot be said that A and B have no intersection, but A∩B=∅.

2. Things to note when performing intersection and union operations on sets

(1) For a set with a limited number of elements, it can be solved directly according to the definition of "intersection" and "union" of the set, but attention should be paid to the mutual heterogeneity of the set elements.

(2) For a set with an infinite number of elements, when performing intersection and union operations, the number axis can be used to solve the problem using the number axis analysis method, but attention should be paid to whether the endpoint value can be obtained.

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

1. Thinking and analysis

(1) The number of elements in set A∪B is the sum of the numbers of all elements in set A and set B. ()

(2) When set A and set B have no common elements, there is no intersection between set A and set B. ()

(3) If A∪B＝A∪C, then B＝C.()

(4)A∩B⊆A∪B.()

2. It is known that the set M={-1,0,1} and P={0,1,2,3}, then the set represented by the shaded part in the figure is ()

A． {0,1}

B． {0}

C. {-1,2,3}

D. {-1,0,1,2,3}

3. It is known that the set A={1,2,3}, B={x|(x+1)(x-2)=0, x∈Z}, then A∩B=()

A． {1}

B． {2}

C. {-1,2}

D. {1,2,3}

Keywords: Free download of PPT courseware for compulsory course 1 of Mathematics in High School People's Education A version, PPT download of basic operations on sets, PPT download of sets and common logical terms, PPT download of union and intersection, .PPT format;

For more information about the PPT courseware "Basic Operations Union and Intersection of Sets and Commonly Used Logic Terms ppt Sets", please click the Basic Operations Union and Intersection ppt of Sets and Commonly Used Logic Terms ppt Sets 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: 2024-07-06

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

Preview