"Basic Operations of Sets" Sets and Common Logic Terms PPT (Complete Collection, Supplements and Comprehensive Applications of Lesson 2)

"Basic Operations of Sets" Sets and Common Logic Terms PPT (Complete Collection, Supplements and Comprehensive Applications of Lesson 2)

Part One: Learning Objectives

Understand the meaning of the complete set and complement, correctly understand the meaning of the symbol ∁UA, and be able to find the complement of the set A when the complete set is known

Able to solve set problems such as intersection, union and complement of sets

Able to correctly use the meaning of complement to solve some specific problems

Basic operations of sets PPT, part 2: independent learning

Problem guide

Preview textbook P12-P13 and think about the following questions:

1. What does the full set mean?

2. What does complement mean?

3. How to understand the meaning of "∁UA"?

4. How to represent ∁UA using Venn diagram?

A preliminary exploration of new knowledge

1. Complete works

(1) Definition: Generally, if a set contains the ______________ involved in the problem under study, then this set is called a complete set.

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

■Instructions from famous teachers

The universe is not a set containing any elements, but only contains all the elements involved in the problem under study.

2. Complement

Literal language For a set A, the set composed of ____________ in the complete set U that does not belong to the set A is called the complement of the set A relative to the complete set U, which is referred to as ____________ and is recorded as _________

Symbolic language ∁UA＝____________________________

graphic language

3. Properties of complements

(1)A∪(∁UA)=____.

(2)A∩(∁UA)=____.

(3)∁UU＝____, ∁U∅＝U, ∁U(∁UA)＝____．

(4)(∁UA)∩(∁UB)＝∁U(A∪B)．

(5)(∁UA)∪(∁UB)＝∁U(A∩B)．

■Instructions from famous teachers

∁UA’s three meanings

(1)∁UA represents a set.

(2)A is a subset of U, that is, A⊆U.

(3)∁UA is the set of all elements in U that do not belong to A.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) The complete set of number set problems must be R.()

(2) The sets ∁BC and ∁AC are equal. ()

(3)A∩∁UA＝∅.()

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

Suppose the set U={1, 2, 3, 4, 5, 6}, M={1, 3, 5}, then ∁UM=()

A． {2, 4, 6} B． {1,3,5}

C. {1, 2, 4} D. U

Assume that the complete set U=R and the set P={x|-1≤x≤1}, then ∁UP=()

A． {x|x＜-1} B. {x|x>1}

C. {x|－1＜x＜1} D. {x|x<-1 or x>1}

It is known that the set A = {3, 4, m}, the set B = {3, 4}, if ∁AB = {5}, then the real number m = ________.

Basic operations of sets PPT, the third part: lecture, practice and interaction

Complement operation

(1) If the complete set U={x∈R|-2≤x≤2}, then the complement ∁UA of the set A={x∈R|-2≤x≤0} is ()

A． {x∈R|0

B． {x∈R|0≤x<2}

C. {x∈R|0

D. {x∈R|0≤x≤2}

(2) Suppose U={x|-5≤x<-2, or 2

Strategies for finding the complement of a set

(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 definition of the complement set. In addition, for such problems, Venn diagrams are often used to solve them during the solution process. When handled in this way, it is relatively intuitive and vivid, and it is less likely to make mistakes when answering.

(2) If the given set is an infinite set, when solving problems related to the complement of the set, the number axis is often used. First, the known set and the complete set are expressed on the number axis respectively, and then the solution is solved according to the definition of the complement.

Comprehensive operations of set intersection, union and complement

(1) (2019•Changsha Test) It is known that the complete set U={1, 2, 3, 4, 5, 6, 7, 8}, set A={2, 3, 5, 6}, set B={1 ,3,4,6,7}, then the set A∩(∁UB)=()

A． {2,5}B. {3,6}

C. {2,5,6} D. {2, 3, 5, 6, 8}

(2) It is known that the complete set U=R, A={x|-4≤x<2}, B={x|-1

Basic operations of sets PPT, Part 4: Feedback on achievement of standards

1. It is known that the complete set U={1, 2, 3, 4, 5, 6}, the set P={1, 3, 5}, Q={1, 2, 4}, then (∁UP)∪Q=()

A． {1}　B． {3,5}

C. {1, 2, 4, 6} D. {1,2,3,4,5}

2. Assume U=R, A={x|x>0}, B={x|x>1}, then A∩(∁UB)=()

A． {x|0≤x<1} B. {x|0＜x≤1}

C. {x|x<0} D． {x|x>1}

3. It is known that the complete set U={1, 2, a2-2a+3}, A={1, a}, ∁UA={3}, then the real number a is equal to ()

A． 0 or 2　B. 0

C. 1 or 2 D． 2

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