Intersection and union of sets.
Kundeleva Oksana Evgenievna
Teacher primary school MBOU NOSH No. 279, Gadzhiyevo, Murmansk region,
Lesson objectives
- form an idea of the union and intersection of two sets
- learn to find on the "map of sets" the area of \u200b\u200bthe set, which is the intersection or union of two sets
- learn to determine the belonging of elements to a set, which is the intersection and union of two sets
- learn to determine the nature of the relationship between two given sets (intersection, do not intersect, union)
- "Months of the Year"
- "Seasons"
- "Continents"
- "Flying hippos"
- Polygons
Bat crow penguin
Butterfly tit ostrich
Read the names of the birds. Circle this set. Make an inscription at the bottom: “Birds”.
Read the names of animals that can fly. Circle this set, make an inscription at the top: "They know how to fly."
can fly
How many elements are on intersection of two sets, i.e. simultaneously in two sets? Why?
Intersection of many common part of sets"AND",
then each of its elements must be on CROSSING two sets -
live in two countries at the same time.
Union of setsIf the name of the set contains the word "OR",
then the element can be anywhere in the territory of two countries - ASSOCIATION -
live in at least one of them.
What is a subset? Subset- this is a part of a set that is part of a given set. Physical education minute One - bend, unbend, Two - bend down, stretch, Three - three clap in the hands, Three nods with the head. Four arms wider, Five, six - sit quietly, Seven, eight - let's discard laziness. Draw sets:Lots of sea creatures
Many mammals
Draw sets:
Lots of birds
Lots of fish
Even numbers live in a square. Two-digit numbers live in a triangle. Write each number correctly. Color in the picture the area where even two-digit numbers live.
2, 47, 16, 8, 17, 32, 6, 53
Find the designation of each set in the table and fill in the circles in the figure.
How many sets are circled? What is the largest set? What color should the largest circle be filled with? What is the largest of the remaining?
Sets:
animals
plants
Find and arrange the elements of the sets in the figures in the figure: write the first letter of each word from the list
Remember!
- Sets do not intersect
The sets do not intersect:
- One set is a subset of another
One set is a subset of another:
The sets intersect:
Multiples are merged:
See you at
next lesson!!!
A.V. Goryachev, K.I. Gorina and others. Informatics in games and tasks, Grade 3, Guidelines for the teacher, M., "Ballas", 2004
- A.V. Goryachev, K.I. Gorina and others. Informatics in games and tasks, Grade 3, Guidelines for teachers, M., "Ballas", 2004
- A.V. Goryachev, K.I. Gorina and others. Textbook "Informatics in games and tasks", grade 3, part 2, M., "Ballas", 2004
- http://festival.1september.ru/articles/505635/ Informatics lesson on the topic "Set. Subset. Intersection of sets" Shchepina Zinaida Nikolaevna, primary school teacher
Used Books
- The set of natural numbers is...
- A lot of 8th grade students are…
- The set of non-positive and non-negative numbers is...
1. Intersection of sets
A=(1,2,3,4,6,8,12,24),
B=(1,2,3,6,9,18),
C is the set of common divisors of numbers 24 and 18,
We say that set C is the intersection of sets A and B.
- The set that makes up the common part of the sets A and B is called the intersection of these sets and is denoted as follows: A∩B=C.
- The ratio between sets A, B and C can be illustrated using special diagrams called Euler circles.
The figure formed at the intersection of circles, shaded in the figure, depicts the set C.
Comment.
Some sets X and Y do not have common elements. Then we say that the intersection of the sets X and Y is the empty set.
Ø is the designation of the empty set.
And then they write like this: X ∩ Y = Ø
For example:
2. Union of sets
A is the set of natural divisors of the number 24,
B is the set of natural divisors of 18.
A=(1,2,3,4,6,8,12,24),
B=(1,2,3,6,9,18),
D is the set to which all elements of set A and all elements of set B belong.
Those. D =(1,2,3,4,6,8,9,12,18,24).
They say that many D is the union of sets A and B.
The sets A and B are shown in circles in the figure.
The figure shaded in the figure is the union of the sets A and B.
For example:
X is the set of prime numbers not exceeding 25;
Y is the set of two-digit numbers not exceeding 19.
Find the intersection and union of sets X and Y.
X=(2, 3, 5, 7, 11, 13, 17, 19, 23);
Y=(10,11,12,13,14,15,16,17,18);
Common elements: 11,13,17, so
X∩ Y =(11,13,17);
X UY =(2, 3, 5, 7,10,11,12,13,14,15, 16,17,18,19,23).
- Solve in class
- № 799
- Solve at home
- № 800
Senina G.N., Senin V.G., MBOU "Secondary School No. 4", Korsakov
MULTIPLE. COMBINATORICS.
INTERCEPTION AND UNION OF SETS.
Metasubject - Knowledge
The purpose of our lesson
In Conan Doyle's story "Five Orange Pips", the famous detective Sherlock Holmes had to establish the name of one sailboat. He only knew about this ship that in January 1883 it was in Pondichshire, in January 1885 - in Dundee, and now it was in London. Comparing the lists of sailing ships that were at the indicated times in the indicated places, Sherlock Holmes established that only the American ship "Lone Star" was included in each of them. As a result, the crime was solved. The detective, having three sets, built a new one containing their common elements. It turned out that the new set consists of only one element
goal setting
Let's check the homework
TEXTBOOK
№ 747
TEXTBOOK
№ 749
P ⊂ N ⊂ Z ; C ⊂ B ⊂ A; K ⊂ P ⊂ R
Entering the topic of the lesson and creating conditions for the conscious perception of new material.
Intersection and Union of Sets
Organization and self-organization of students. Organization feedback
Working with text
TRAINING APPARATUS
№ 319
to each of these sets
Workshop
Working with text
TRAINING APPARATUS
№ 320
Workshop
Working with models
TRAINING APPARATUS
№ 323
Workshop
Working with models
TRAINING APPARATUS
№ 324
Workshop
Operations on sets
PROBLEM
№ 638
PROBLEM
№ 639
Workshop
Operations on sets
PROBLEM
№ 641
{-1,0,1}; {-5,-4,-3,-2,-1,0,1,2}
{-1,0}; {-4,-3,-2,-1,0,1}
{1}; {-2,-1,0,1,2,3,4}
{-1,0,1}; {-2,-1,0,1,2}
Workshop
Operations on sets
TEXTBOOK
№ 757
Properties of zero when multiplying and adding numbers: A ⋅ 0 = 0; A + 0 = A.
Workshop
Operations on sets
TEXTBOOK
№ 758
Operations on sets
№ 760
TEXTBOOK
Checking the results. Correction
Multitudes and Life
A set is a fundamental concept not only of mathematics, but of the whole world around.
Take any item in your hand right now. Here you have a set consisting of one element.
Take a large bag and start randomly putting various items into it.
There is no regularity in this, but, nevertheless, we are talking about a variety of subjects.
Homework U: pp. 228 - 229, fragment 1 - read;
№ 751, 752, 756, 759.
Summing up, reflection, homework.
Sets. Operations on sets
LOTS OF
FIND THE UNION OF SETS
ELEMENT OF THE SET
TYPES OF SET
FIND THE INTERCEPTION OF SETS
RELATIONS BETWEEN
MULTIPLE
DRAW WITH THE HELP OF EULER CIRCLES
“Many is many, thought by us as one”
founder of set theory
Georg Kantor
Set Theory Concepts
The concept of a set is one of the most general and most important mathematical concepts. It was introduced into mathematics by the German scientist Georg Cantor (1845-1918). Following Cantor, the concept of "set" can be defined as follows:
- A set is a collection of objects that have a certain property, united into a single whole.
SET OF PENCILS
THE COLLECTION OF POSTMARKS
FLOCK OF BIRDS
HERD OF COWS
TEA-SET
BOUQUET OF FLOWERS
A set is a collection of objects united according to some attribute.
Sets are denoted by capital letters of the Latin alphabet: A, B, C, D, etc.
The objects that make up a set are called elements of the set.
lots of
element
Trapezoid, parallelogram, rhombus, square, rectangle
Ball, cuboid, prism, pyramid, octahedron
Integers
1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ..
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Two-digit even numbers
Many quadrilaterals
Spatial bodies
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11…
Number squares
Decimal digits
10, 12, 14, 16 … 96, 98
many people in the sun
set of right angles of an equilateral triangle
set of intersection points of two parallel lines
An empty set is a set that does not contain any elements.
Designations of some numerical sets:
N is the set of natural numbers;
Z is the set of integers;
Q is the set of rational numbers;
I - set of irrational numbers;
R is the set of real numbers.
TYPES OF SET
Write down the letters of the words
HORSES AND KINO
{ K, O, N, I }
{ MOVIE }
Equal Sets
TYPES OF SET
A \u003d (2; 3; 5; 7; 11; 13);
finite sets
TYPES OF SET
{1; 4; 9; 16; 25; …};
{10; 20; 30; 40; 50; …};
Infinite sets
Among the sets listed below, indicate the finite and infinite sets:
a) the set of numbers that are multiples of 13;
b) the set of divisors of the number 15;
c) many trees in the forest;
d) the set of natural numbers;
e) many rivers of the Rostov region;
f) the set of roots of the equation x + 3 = 11;
g) the set of solutions to the inequality x + 1 
Specify the set of digits with which the number is written:
a) 3254; b) 8797; c) 11000; d) 555555.
Describe set A:
a) A = (1, 3, 5, 7, 9);
b) A \u003d (- 2, - 1, 0, 1, 2);
c) A = (11, 22, 33, 44, 55, 66, 77, 88, 99);
Given a set:
M = (5, 4, 6),
P = (4, 5, 6),
T = (5, 6, 7),
S = {4, 6}.
Which of the statements is incorrect?
a) M = R b) R ≠ S c) M ≠ T d) P = T
Let BUT is the set of prime numbers of the form
7n + 2, where n ∈ N.
Is the notation -5 ∈ A correct?
1. In the set (lion; fox; hyena; elephant; lynx) all elements except one have some property. a) describe this property; b) find an element that does not have this property; c) Name two more elements that have this property. 2. Name 5 subsets in the set of all the colors of the rainbow. 3. What property in set of rhombuses, a subset of squares stands out?
Example: 8 and 32
BLITZ POLL
- amphibians, mammals, cold-blooded animals, etc.
What names are used to refer to many animals?
BLITZ POLL
- company, platoon, regiment, division, etc.
What names are used to refer to sets of military personnel?
BLITZ POLL
- bouquet
What is the name of the many flowers in a vase?
BLITZ POLL
- equator
What is the name of the set of points on the earth's surface that are equidistant from both poles?
BLITZ POLL
- village, village, town, town
What is the name of the many places inhabited by people?
BLITZ POLL
- exhibition, gallery
What is the name of the set of pictures?
BLITZ POLL
- archive
What is the name of the set of documents?
BLITZ POLL
- flotilla, squadron
What names are used to designate sets of ships?
A - even natural numbers B - two-digit numbers
Find the union of these sets.
A B - be an even natural or two-digit number
Example: 8 and 32
A - even natural numbers B - two-digit numbers
Find the intersection of these sets.
A B - be an even natural and two-digit number
Example: 32
Given a set:
A \u003d (2; 3; 8),
B = (2; 3; 8; 11),
C = (5; 11).
Find: 1) AUB; 2) AUC; 3) CUB.
Given a set:
A = ( a , b , c , d },
B = { c , d , e , f },
C = { c , e , g , k }.
Find: (AUB)UC.
Given a set:
A is the set of all natural numbers divisible by 10,
B \u003d (1; 2; 3; ..., 41).
Find A∩B.
The solution of the problem
using Euler circles
Leonard Euler- Swiss, German and Russian mathematician, who made a significant contribution to the development of mathematics, as well as mechanics, physics, astronomy and a number of applied sciences.
There are 30 people in the class, each of whom sings or dances. It is known that 17 people sing, and 19 people know how to dance. How many people are singing and dancing at the same time?
dance 19
17+19=36, total 30
Solution
Let A be the set of students who can sing. The number of elements in it, by condition, is equal to n = 17. Let B be the set of students who can dance. The number of elements in it is m = 18. The set coincides with the whole class, because every student in the class sings or dances. - this is the set of those students of the class who sing and dance at the same time. Let their number be equal to k .
According to the formula proved above
n + m- k = 17+ 19- k = 30 k = 6.
Answer: 6 students in the class sing and dance at the same time.
The company employs 67 people. Of these, 47 know English, 35 - German, and 23 are both languages. How many people in the company do not know either English or German?
German 35
English 47
Each student in the class learns English or French. English language 25 students study French, 27 students, and 18 students study two languages. How many students are in the class?
German 27
English 25
German only
English only
Answer: there are 34 students in the class
The sets A and B contain 5 and 6 elements, respectively, and the set A ∩ B contains 2 elements. How many elements are in set A U AT?
Union contains 9 elements
Each family living in our house prescribes or
newspaper, or magazine, or both. 75 families
subscribe to the newspaper, and 27 families subscribe to the magazine, and only 13 families subscribe to both the magazine and the newspaper. How many families live in our house?
Total: 14 + 13 + 62 = 89
At the school sports day, each of the 25 students on the 9th
class fulfilled the standard either in running or in high jump. Both standards were fulfilled by 7 people, and 11 students completed the standard for running, but did not fulfill the standard for high jumps. How many students completed the standard: a) in running; b) high jump; c) for jumps, provided that the standard for running is not fulfilled?
On Sunday, 19 students from our class visited
planetariums, 10 in the circus and 6 in the stadium. The planetarium and the circus were visited by 5 students; planetarium and stadium - 3; circus and stadium - 1. How many students are in our class if no one managed to visit all three places, and three students did not visit any place?
LOTS OF
FIND THE UNION OF SETS
ELEMENT OF THE SET
TYPES OF SET
FIND THE INTERCEPTION OF SETS
RELATIONS BETWEEN
MULTIPLE
DESIGN USING EULE-VENN CIRCLES
SOLVING PROBLEMS USING EXISTING KNOWLEDGE
Presentation on the topic "Intersection and union of sets" (optional "Visual geometry" (Grade 3).
Usage information technologies not only revived the educational process (which is especially important given the psychological characteristics of the younger school age, in particular, the long-term predominance of visual-figurative thinking over abstract-logical), but also increased the motivation for learning in the classroom.
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Intersection and union of sets. Kundeleva Oksana Evgenievna Primary school teacher MBOU NOSH No. 279, Gadzhiyevo, Murmansk region, 2012
The objectives of the lesson are to form an idea of \u200b\u200bthe union and intersection of two sets, to learn to find on the "set map" the area of \u200b\u200bthe set, which is the intersection or union of two sets, to learn to determine the belonging of elements to the set, which is the intersection and union of two sets, to learn to determine the nature of the relationship between two given sets (intersection , disjoint, union)
What is a set? A set is a group of items, objects, or beings.
Name the elements of the set: “Months of the year” “Seasons” “Continents” “Flying hippos” Polygons
Wasp Bat Crow Penguin Butterfly Tit Ostrich Sparrow Read the names of the birds. Circle this set. Make an inscription at the bottom: “Birds”. BIRDS Read the names of animals that can fly. Circle this set, make an inscription at the top: "They know how to fly." can fly How many elements are at the intersection of two sets, i.e. simultaneously in two sets? Why?
Intersection of sets - common part of sets If the name of a set contains the word "AND", then each of its elements must be at the INTERSECTION of two sets - to live simultaneously in two countries. !
Union of sets If the name of the set contains the word "OR", then the element can be anywhere in the territory of two countries - UNION - live in at least one of them. ! ! ! !
What is a subset? A subset is a part of a set that is part of a given set.
Physical education minute One - bend, unbend, Two - bend down, stretch, Three - three clap in the hands, Three nods with the head. Four arms wider, Five, six - sit quietly, Seven, eight - let's discard laziness.
A lot of sea inhabitants A lot of mammals Draw a set:
Draw Sets: Many Birds Many Fishes
Even numbers live in a square. Two-digit numbers live in a triangle. Write each number correctly. Color in the picture the area where even two-digit numbers live. 2, 47, 16, 8, 17, 32, 6, 53 2 47 16 8 17 32 53 6
Find the designation of each set in the table and fill in the circles in the figure. Sets: rectangles quadrangles polygons squares How many sets are circled? What is the largest set? What color should the largest circle be filled with? What is the largest of the remaining?
Sets: Animals Animals Fish Birds Plants Seagull Fox Iceberg Giraffe Pine River Tulip Ant Flounder Find and arrange the elements of the sets in the figures in the picture: write the first letter of each word from the list
C K M T R S J A L
Remember! Sets do not intersect Sets do not intersect: One set is a subset of another One set is a subset of another: Sets intersect: Sets combine:
See you in the next lesson!!!
A.V. Goryachev, K.I. Gorina and others. Informatics in games and tasks, Grade 3, Guidelines for teachers, M., "Ballas", 2004 A.V. Goryachev, K.I. Gorina and others. Textbook "Informatics in games and tasks", grade 3, part 2, M., "Ballas", 2004 http://festival.1september.ru/articles/505635/ Informatics lesson on the topic "Set. Subset. Intersection of sets" Shchepina Zinaida Nikolaevna, primary school teacher
