O’zbekiston respublikasi oliy va o’rta maxsus ta’lim vazirligi termiz davlat pedagogika instituti matematika va uni o’qitish metodikasi kafedrasi algebra va sonlar nazariyasi fanidan mustaqil ta’lim topshiriqlari to’plami

3-MISOL. Ixtiyoriy A,B va C to‘plamlar uchun ushbu
Ax (BC) = (AxB)(AxC)
munosabatning to‘g‘ri ekanligini isbotlang.
a) ixtiyoriy Ax(BC) bo‘lsin, bundan xA, yBCbo‘lganligi uchun, birlashmani ta’rifidan xA, yB yoki yC. SHunday qilib, xA va yB yoki xA va yC, bulardan va to‘g‘ri ko‘paytmaning ta’rifidan AxB yoki Ax C
Demak,  (A x B)  (AxC), ya’ni
A x (BC) (AxB)(AxC) (2)
b) ixtiyoriy (A x B)(AxC) bo‘lsin. Bundan (A x B)yoki (AxC). To‘g‘ri ko‘paytmaning ta’rifidan xA va uB yokixA va uB bulardan xA va uBC. Demak, Ax (BC) yoki
(AxB)(AxC)Ax(BC) (3)
(2) va (3) munosabatlardan (1) tenglikni o‘rinli ekanligi kelib chiqadi.
To‘plamlar ustida amallarni bajaring .


1). [8;15]  [9;20]; [-1;1]  [-1;0); (-1-.0] [l;+);


2).[1;+) [0;); [-1;0)  [0;4]; {4} (-;4);


3).(0:2)  [0;2); [3;15] \ (5;16); [3;16]\[5;15];
[3;5][2;7]; [2;5] [3;7].


Tengliklarni isbotkfng .


4).A\(BC)=(A\B)(A\C);


5) (AB)\(AB)=(A\B) (B\A);


6). A\(BC)=(A\B) (A\C);


7) A\(A\B)=AB;


8).A\B=A\(AB);


9)A (B\C)=(AB)/C;


10). A (B\C)=(AB)\(AC);


11)A (B\A)=AB;


12). A\B=(AB)\B ;


13). (A\B)\C=A\(BC);


14).A\(B\C)=(A\B) (AC);


15) (A\B)C=(AC)\(BC).


16) (A\B)\C=(A\C)\(B\C) ;


17) A\(B\C)AC ;


18) (A\C)\(B\A)A\C ;