"Basic Relationships Between Sets" Sets and Common Logic Terms PPT Download

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"Basic Relationships Between Sets" Sets and Common Logic Terms PPT Download

Part One: Learning Objectives

1. Understand the meaning of inclusion and equality between sets. (emphasis)

2. Be able to identify subsets and true subsets of a given set, and be able to judge the relationship between sets. (Difficult, easy to confuse)

3. Understand the meaning of the empty set in specific situations. (difficulty)

core competencies

1. Cultivate mathematical abstract literacy through understanding the meaning of inclusion and equality between sets, as well as the concepts of subsets and proper subsets.

2. Cultivate mathematical operations literacy with the help of solving subsets and proper subsets.

PPT on the basic relationship between sets, part 2: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

1. Advantages and representation of Venn diagrams

(1) Advantages: Intuitive image.

(2) Representation: Usually ______ of ______ is used to represent a set.

2. Related concepts of subsets, proper subsets, and set equality

Thinking 1: (1) Is there an inclusion relationship between any two sets?

(2) What is the difference between the symbols "∈" and "⊆"?

Tips: (1) Not necessarily. For example, the set A={0,1,2} and B={-1,0,1}, there is no inclusion relationship between these two sets.

(2) The symbol “∈” represents the relationship between elements and sets;

And "⊆" represents the relationship between sets.

3. empty set

(1) Definition: A set that does not contain ______ elements is called an empty set and is recorded as ______.

(2) stipulation: ______ is a subset of any set.

Thinking 2: Is {0} the same as ∅?

Tip: Different. {0} represents a set, and there is and is only one element 0 in the set; and ∅ represents the empty set, which does not contain any elements, so {0}≠∅.

4. The nature of the relationship between sets

(1) Any set is a subset of itself, that is, A⊆A.

(2) For the set A, B, C,

①If A⊆B, and B⊆C, then A⊆C;

②If A B, B C, then A C.

(3) If A⊆B, A≠B, then A B.

First try

1. Assume the set M={1,2,3}, N={1}, then the following relationship is correct ()

A． N∈M

B． N∉M

C. N⊇M

D. N⊆M

2. Among the following four sets, the one that is the empty set is ()

A． {0}

B． {x|x>8, and x<5}

C. {x∈N|x2－1＝0}

D. {x|x>4}

3. There are _________ subsets of the set {0,1}.

4. It is known that the set A={x|x2-3x+2=0}, B={1,2}, C={x|x<8, x∈N}, fill in the blanks with appropriate symbols:

(1)A________B; (2)A________C;

(3){2}________C; (4)2________C.

PPT on the basic relationship between sets, the third part: cooperative exploration to improve literacy

Judgment of relationships between sets

[Example 1] Determine the relationship between the sets in the following groups:

(1) A={x|x is a divisor of 12}, B={x|x is a divisor of 36};

(2) A={x|x is a parallelogram}, B={x|x is a rhombus}, C={x|x is a quadrilateral}, D={x|x is a square };

(3)A={x|-1

[Solution] (1) Because if x is a divisor of 12, it must be a divisor of 36, and vice versa, so A B.

(2) Based on the characteristics of the graph, the Venn diagram can be drawn as shown in the figure, so that D B A C.

(3) It is easy to know that the elements in A are all elements in B, but there are elements, such as -2∈B, but -2∉A, so A B.

regular method

Methods to determine set relationships.

1Observation method: List observations one by one.

2Element characteristic method: First determine what the elements of the set are, clarify the characteristics of the set elements, and then use the characteristics of the set elements to determine the relationship.

3Number-shape combination method: Use number lines or Venn diagrams.

Reminder: If A⊆B and A B are true at the same time, then A B can more accurately express the relationship between sets A and B.

PPT on the basic relationship between sets, the fourth part: meeting the standards in class and solidifying the two bases

1. Thinking and analysis

(1) There is only element 0 in the empty set and no other elements. ()

(2) Any set has subsets. ()

(3) If A=B, then A⊆B or B⊆A.()

(4) The empty set is a proper subset of any set. ()

2. The number of proper subsets of the set A={x|0≤x<3, x∈N} is ()

A． 16B. 8

C. 7 D． 4

3. It is known that the set A={-1,3,m}, B={3,4}, if B⊆A, then the real number m=________.

4. It is known that the set A={x|1≤x≤2}, B={x|1≤x≤a, a≥1}.

(1) If A B, find the value range of a;

(2) If B⊆A, find the value range of a.

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Update Time: 2024-10-09

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

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