Understand the meaning of complete works, understand the concept of complementary sets, and express the relationship between sets with venn diagram; Infiltrate the relative viewpoint.
Teaching focus:
The concept of complement set.
Teaching difficulties:
Related operations of complementary sets.
Category type:
New teaching
Teaching methods:
Discover the teaching method, by introducing examples, and then analyzing the examples, find out the general results and summarize its general rules.
Teaching process:
First, create a situation
1. Review Introduction: Review the concepts of set, subset and set equality; The intersection and union of two sets.
2. Relative to a set U, the elements in its subset are part of U, so the remaining elements should also form a set. These two sets constitute a relative relationship to U, which verifies that "everything is a relationship of unity of opposites". The relationship between some elements in a set and the set is the relationship between parts and the whole. This is the theme of this lesson-complete works and addenda.
Second, the new lesson explanation
Please give a similar example.
For example, u = {the whole class} A = {the boys in the class} B = {the girls in the class}
Feature: Set B is the remaining set after set A is removed from set U, which can be represented by venn diagram.
We call b the complement of a to the complete set u.
1, complete works
If the set S contains all the sets we want to study, then S can be regarded as a complete set. A complete work is usually represented by the letter u.
2. Complement set (remainder set)
Let U be a complete set and A be a subset of U (that is, A U), then the set composed of all elements in U that do not belong to A is called "A's complement set in U", which is referred to as the complement set of Set A for short, and is denoted as, namely
Venn diagram representation of complement set;
Note: the concept of complement set must be limited by complete set.
Exercise:
3. Basic nature
Note: Illustrated by venn diagram.
Third, give an example
Case 1(P 13 case 3)
Example 2(P 13 Example 4) ① Pay attention to the operation of the set with the help of the number axis ② Verify the basic properties with the results.
Fourth, classroom exercises.
1. For example, please fill in (refer to).
(1) if S = {2 2,3,4} and A = {4 4,3}, then SA = _ _ _ _ _ _ _ _ _
(2) If S = {triangle} and B = {acute triangle}, then SB = _ _ _ _ _ _ _ _
(3) If S = {1, 2,4,8} and A =, then SA = _ _ _ _ _
(4) If U = {1, 3, A2+2A+ 1}, A = {1, 3}, UA = {5}, then A = _ _ _ _ _ _ _ _
(5) Given A = {0 0,2,4}, UA = {- 1, 1}, UB = {- 1, 0,2}, find B = _ _ _ _ _
(6) Let the complete set U = {2 2,3,2+2-3}, A = {|+ 1 |, 2}, UA = {5}, and find.
(7) Let the complete set U = {1, 2,3,4}, A = {x | x2-5x+= 0, x∈U} to find UA.
Teachers and students work together to solve the above problems, and the basis for solving problems is definition.
Example (1) solution: sa = {2}
Comment: Mainly compare the differences between A and S.
Example (2) Solution: SB = {right triangle or obtuse triangle}
Comments: Pay attention to triangle classification.
Example (3) Solution: SA = 3
Comment: Definition and application of empty set.
Example (4) solution: A2+2A+ 1 = 5, A =- 1.
Note: Take advantage of the characteristics of set elements.
Solution of Example (5): Use venn diagram to find U = {- 1 0, 1, 2,4} from A and UA, and then find B = {1, 4}.
Solution of example (6): that solution of problem 2+2-3 = 5 and |+ 1 | = 3 is =-4 or = 2.
Example (7) solution: substitute x = 1, 2,3,4 into x2-5x+= 0, = 4 or = 6.
When = 4, x2-5x+4 = 0, that is, A = {1, 4}
When = 6, x2-5x+6 = 0, that is, a = {2 2,3}
Therefore, the problem condition is satisfied: UA = {1, 4}, = 4; UB={2，3}，=6 .
Comments: In the process of solving this problem, the idea of classified discussion runs through.
2. Exercise 1, 2, 3, 4, 5
Review and reflection on verb (abbreviation of verb)
This section mainly introduces complete set and complementary set, which is based on the concept of subset and introduces the concept of complete set.
1, the complete set is a relative concept, which contains all the elements of each set related to the research problem, and is usually represented by "u". Studying different problems, the complete works are not necessarily the same.
2. Complement set is also a relative concept. If the set A is a subset of the set S, the set consisting of all elements in S that do not belong to A is called the complement of the subset A in S, and it is recorded as ={x|}. When s is different, the complement of set A is also different.
Six, homework arrangement
1, 15 Exercise 4,5
2. Use the intersection, union and complement of sets A, B and C to represent the set represented by the colored part in the figure below.
3, thinking: p 15 B group problem 1, 2