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

Description

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

Part One: Learning Objectives

1. Understand the meaning of intersection and union of two sets, and be able to find the intersection and union 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. Improve your mathematical abstract literacy by understanding the concepts of set intersection and union.

2. Cultivate the ability of intuitive imagination with the help of Venn diagrams.

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

1. intersection

2. 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 a Venn diagram to represent it as shown in the figure.

(2) is not equal to. 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.

3. Operational properties of union and intersection

First try

1. Assume set A={0,1,2,3} and set B={2,3,4}, then A∩B=()

A． {2,3}B． {0,1}

C． {0,1,4} D. {0,1,2,3,4}

2. It is known that the set M={0,1,3}, N={x|x=3a, a∈M}, then M∪N=()

A． {0} B. {0,3}

C． {1,3,9} D. {0,1,3,9}

3. (2018•National Volume III) It is known that the set A={x|x-1≥0}, B={0,1,2}, then A∩B=()

A． {0}B． {1}

C． {1,2} D. {0,1,2}

4. Set A={0,2,a}, B={1,a2}, if A∪B={0,1,2,4,16}, then the value of a is ________.

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

The concept of intersection and its applications

[Example 1] (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. 4

C． 3D． 2

regular method

1. Methods for calculating the intersection of sets

(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. However, it should be noted that when expressing inequalities using a number line, values ​​containing endpoints are represented by solid points, and values ​​without endpoints are represented by hollow points.

The concept of union and its applications

[Example 2] (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|－3

D. {x|x<-3 or x>5}

regular method

Two basic methods for finding the union of sets

1 Definition method: If the set is represented by the 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.

Properties and comprehensive applications of set intersection and union operations

[Inquiry Questions]

1. Suppose A and B are two sets. If A∩B=A and A∪B=B, what is the relationship between sets A and B?

Tip: A∩B＝A⇔A∪B＝B⇔A⊆B.

2. If A∩B=A∪B, what is the relationship between sets A and B?

Tip: If A∩B=A∪B, then the set A=B.

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" the 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 It is 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 is 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}

4. Suppose A={x|x2+ax+12=0}, B={x|x2+3x+2b=0}, A∩B={2}, C={2,-3}.

(1) Find the values ​​of a, b and A, B;

(2) Find (A∪B)∩C.

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Update Time: 2024-11-22

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