"Basic Operations of Sets" Sets and Common Logic Terms PPT Courseware (Supplement to the 2nd Lesson)

Description

"Basic Operations of Sets" Sets and Common Logic Terms PPT Courseware (Supplement to the 2nd Lesson)

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 complements.

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 to explore new knowledge

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 written as ____.

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

Tip: The universal set is a relative concept and 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=

graphic language

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}.

Method 2 (Venn diagram method): The Venn diagram that meets the meaning of the question is as shown in the figure.

It can be seen from the figure that B={2,3,5,7}.

(2) Express the set U and set A on the number axis respectively, as shown in the figure.

From the definition of complement, we can know that ∁UA={x|x<-3 or x=5}. ]

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 it directly.

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

3 Number line method: When the elements in the set are continuous and infinite, you can use the number line 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=______.

(1)C　(2){x|0

(2) As shown in the figure, two sets are represented on the number axis respectively. From the definition of the complement set, it can be seen that ∁UA={x|0

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

B． {x|x≤-4}

C. {x|x≤1}

D. {x|x≥1}

Keywords: Free download of PPT courseware for compulsory course No. 1 Mathematics of 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 complementary sets, .PPT format;

For more information about the PPT courseware "Basic Operations Complements of Sets and Commonly Used Logic Terms ppt Sets", please click the Basic Operations ppt Complements of Sets and Commonly Used Logic Phrases ppt tag.

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Update Time: 2024-06-19

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

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