1. Teng to’plamlar. To’plam osti. Universal to’plam

Elementar munosabatlar

To`plamlar bilan ishlaganda, “x ni A to`plamning elementi deb hisoblaymiz, shu narsa o`rinliki va bu tasdiq quydagicha belgilanadi x<sub></sub>A. Shunday qilib, agar Z butun sonlar to`plami bo`lsa biz quyidagi tasdiqlarni yozishimiz mumkin 3_Z, -11_Z, va hokazo. Bundan tashqari _ butun son emas, shuning uchun biz uni quyidagicha yozamiz _Z²_.

Elementary relationships

When dealing with sets nai vely ,we shall assume that the statement “x in an element of the set A”makes sens and shall symbolically denote this stastment by writing x _ A.Thus, if Z denotes the set of integers , we can write such statements as 3 _ Z ,-11 _ Z ,and so on. Likewise, _ is not an integer so we’ll express this by writing _ Z .

In the vast majority of our considerations we shall be considering sets in a given “context”, i..e..,as subsets of a given set. thus ,when I speak of the set of integers ,I am usually referring to a particular subset of the real numbers .The point here is that while we might not really know what a real number is (and therefore we don’t really “understand” the set of real numbers ),we probably have a better understanding of the particular subset consisting of integers (whole numbers ).Anyway ,if we denote by R the set of all real numbers and write Z for the subset of of integers ,then we can say that.

Mustaqil o’rganish uchun savоllar

1. 
   To‘plam deganda nimani tushunasiz?
   
2. 
   Bo‘sh, chekli, cheksiz to‘plamlarga misollar keltiring.
   
3. 
   To‘plamlar necha xil usulda beriladi?
   
4. 
   Teng to‘plamlarga ta’rif bering.
   
5. 
   To‘plam osti tushunchasiga ta’rif bering va misollar keltiring.
   
6. 
   Qanday to‘plamlar ekvivalent to‘plamlar deyiladi va qanday qilib ikki to‘plam orasida ekvivalentlikni o‘rnatish mumkin.
   
7. 
   Universal to‘plam deganda qanday to‘plamni tushunasiz? Misollar keltiring.
   

Foydalaniladigan asosiy adabiyotlar ro‘yxati

Asosiy adabiyotlar

1. 
   Xamedova N.A, Ibragimova Z, Tasetov T. Matеmatika. Darslik. T.: Turon-iqbol, 2007. 363b. (10-13 bet)
   

Qo‘shimcha adabiyotlar

1. 
   Abdullayeva B.S., Sadikova A.V., Muxitdinova M.N., Toshpo‘latova M.I., Raximova F. Matematika. TDPU. (Boshlang‘ich ta’lim va sport-tarbiyaviy ish bakalavriyat ta’lim yo‘nalishi talabalari uchun darslik) Toshkent-2012, 284 bet (9-13 bet)
   
2. 
   David Surovski Advanсed High-School Mathematics. 2011. 425s. (187-188 bet)
   

To`plamlarning bеrilish usullari. Tеng to`plamlar. To`plam osti. Univеrsal to`plam. Eylеr-Vеnn diagrammalari.

Reja:

1.To`plamlarning berilish usullari.

2.Teng to`plamlar. Universal to`plam.

3. Eyler-Venn diagrammalari.
Namuna:A={a,b,c}to’plаmning bаrchа qism to’plаmlаrini tоping.

Yechilishi: {Ø, {a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}}

1-misоl.A={0,1,2,3,4} to’plamning barcha qism to’plamlarini yozing va ular sonini aniqlang.

B= {a; b; c; d} to’plamning barcha qism to’plamlarini yozing va ular sonini aniqlang.

2-misоl.AgarA = {x | x∈N, x< 72} bo’lsa, shu to’plamning

12 ga karrali;

9 ga karrali;

5 ga karrali bo’lmagan;

4 ga va 3 ga karrali sonlarda tuzilgan qism to’plamlarini aniqlang.

3-misоl.Quyidagi to’plamning nega bo‘sh to’plam ekanligini tushuntiring:

Quyidagi to’plamning nega bo‘sh to’plam ekanligini tushuntiring:

a) {x / xN, x 1};

b) {x / xN, 15 x 16};

d) ;

e) {x / x 7, x 5}.