1-amaliy mashg’ulot mavzu: Toʼplamlar va ular ustida amallar. Eyler-Venn diagrammalari. Toʼplamning quvvatini topishga doir masalalar yechish. Munosabatlar ustida amallar. Munosabatlar kompozitsiyasi. Binar munosabatlar va ularning matritsalarini

1-AMALIY MASHG’ULOT


MAVZU: Toʼplamlar va ular ustida amallar. Eyler-Venn diagrammalari. Toʼplamning quvvatini topishga doir masalalar yechish.Munosabatlar ustida amallar. Munosabatlar kompozitsiyasi. Binar munosabatlar va ularning matritsalarini topish.Munosabatlarning turlarini aniqlash. Refleksivlik. Simmetriklik. Tranzitivlik. Аntisimmetriklik. Ekvivalent munosabatlarni aniqlashga doir misollar yechish.Аkslantirishlar. Inʼektiv, syurʼektiv, biektiv funktsiyalar. Funktsiya turlarini aniqlashga doir misollar yechish

Quyidagi misollarnig shartlarida Universal to‘plam U={ a, b, c,

d, e, f, g,h } da X va Y to‘plamlar berilgan bo‘lib,


X  Y , ^Y ,

^XY ,
^{X ∩ Y} ,


X \ Y
to‘plamlarni A, B, C lar orqali

ifodalang va Eyler-Venn diagrammalrida tasvirlang.

1.1.0	X={a,b,c,d}, Y={b,c,d,e}	1.1.10	X={c,d,e,f}, Y={e,f,g,h}	1.1.20	X={e,f,g,h}, Y={h,a,b,c}
1.1.1	X={b,c,d,e}, Y={c,d,e,,f}	1.1.11	X={d,e,f,g}, Y={f,g,h,a}	1.1.21	X={f,g,h,a}, Y={a,b,c,d}
1.1.2	X={c,d,e,,f}, Y={d,e,f,g}	1.1.12	X={e,f,g,h}, Y={g,h,a,b}	1.1.22	X={g,h,a,b}, Y={b,c,d,e}
1.1.3	X={d,e,f,g}, Y={e,f,g,h}	1.1.13	X={f,g,h,a}, Y={h,a,b,c}	1.1.23	X={h,a,b,c}, Y={c,d,e,,f}
1.1.4	X={e,f,g,h}, Y={a,f,g,h}	1.1.14	X={g,h,a,b}, Y={a,b,c,d}	1.1.24	X={a,b,e,f}, Y={c,d,e,,f}
1.1.5	X={a,,f,g,h}, Y={a,b,g,h}	1.1.15	X={h,a,b,c}, Y={b,c,d,e}	1.1.25	X={b,c,f,g}, Y={d,e,,f,g}
1.1.6	X={a,b,g,h}, Y={a,b,c,h}	1.1.16	X={a,b,c,d}, Y={d,e,f,g}	1.1.26	X={c,d,g,h}, Y={e,g,h,a}
1.1.7	X={a,b,c,h}, Y={a,b,c,d}	1.1.17	X={b,c,d,e}, Y={e,f,g,h}	1.1.27	X={d,e,h,a}, Y={g,h,a,b}
1.1.8	X={a,b,c,d}, Y={c,d,e,,f}	1.1.18	X={c,d,e,f}, Y={f,g,h,a}	1.1.28	X={e,f,a,b}, Y={h,a,b,c}
1.1.9	X={b,c,d,e}, Y={d,e,f,g}	1.1.19	X={d,e,f,g}, Y={g,h,a,b}	1.1.29	X={f,g,b,c}, Y={a,b,c,d}

0-topshiriqnig ishlanishi
1.1.0. U={ a, b, c, d, e, f, g,h } da X={a,b,c,d} va Y={b,c,d,e} to‘plamlar berilgan

bo‘lib,

X  Y , ^Y ,
^XY ,
X ∩ Y _,


X \ Y

to‘plamlarni A, B, C lar orqali

ifodalang va Eyler-Venn diagrammalrida tasvirlang.
X Y  a,b, c, db, c, d, e a,b, c, d, e f , g, h A  B  A  B  C
Y  b, c, d, e a, f , g, h A  B  C  A  B  A  B  C
X Y  a,b, c, db, c, d, e e, f , g, hb, c, d, e b, c, d, f , g, h
 B  AC


X  Y  a, b, c, d b, c, d, e a, b, c, d a, f , g, h a
 A  B  C


X \ Y  a,b, c, d\ b, c, d, e e, f , g, h\ a, f , g, h e A  B  C
2. Murakkab to‘plamlarni soddalashtirish

1.2.0	(A ∪ B ∩ A) ∩ (A ∪ A ∩ B)		1.2.15	( A 𝖴 B)∩( B 𝖴A∩C)
1.2.1			1.2.16
1.2.2			1.2.17
1.2.3	( A \ B ∪ A ∩ B) ∩ А		1.2.18
1.2.4	(B\A) ∩ ( B\A)		1.2.19	A∩(A∩B𝖴 A ∩ B )∩( A 𝖴 C )
1.2.5	A  B \ С  A  B \ С		1.2.20
1.2.6	A  B \ С  A  B \ С		1.2.21
1.2.7	A  B  A  B		1.2.22
1.2.8			1.2.23
1.2.9			1.2.24	A∩( A ∩B𝖴 C)∩(A𝖴 C )
	1.2.10	A (B
	1.2.11	А ∩ (А ∪ В ∩ С) ∩ В ∩ С ∪ А ∩ В ∩ С
	1.2.12	С ∩ (С ∪ В ∩ А) ∩ В ∩ А ∪ С ∩ В ∩ А
	1.2.13
	1.2.14	A/ B ∪ A/ C ∪ A/ B / C ∩ A ∩ B ∩ C
	1.2.25
	1.2.26
	1.2.27
	1.2.28
	1.2.29

Yuqorida keltirilgan soddalashtirishlarni amalga oshirish uchun quyida keltirilgan to‘plamlar ustida amallar xossalaridan foydalaning:
U-universаl to‘plаmning А, B, C to‘plаm оstilаri uchun quyidаgi хоssаlаr o‘rinli

1.	A ∪ B  B ∪ A		Kоmmutаtivlik		11.		А ∩ А  А
2.	A ∩ B  B ∩ A				12.		А ∪ А  U		0 vа 1 qоnunlаri
3.	(A ∪ B) ∪ C  A ∪ (B ∪ C)		Аssоtsiаtivlik		13.		А ∩ А  Ø
4.	(A ∩ B) ∩ C  A ∩ (B ∩ C)				14.		А ∪ Ø=A
5.	(A ∪ B) ∩ C  (A ∩ C) ∪ (B ∩ C)		distributivlik		15.		А ∩U  A
6.	(A ∩ B) ∪ C  (A ∪ C) ∩ (B ∪ C)				16.		А ∪U  U
7.	A ∩ (A ∪ B)  A	Yutilish qоnunlаri		17.		А ∩ Ø= Ø
8.	A ∪ (A ∩ B)  A				18.		U  Ø
9.	А ∩ В  А ∪ В	De Mоrgаn qоnunlаri		19.		=U
10.	А ∪ В  А ∩ В				20.		A\ B  A ∩ B
	21.	A  A	Ikkilаngаn rаd etish qоnuni

1.2.0-variant


(A ∪ B ∩ A) ∩ (A ∪ A ∩ B)  6  xossaga _ ko' ra  (A  B)  (A  A)  (A  A)  (A  B) 
=12-xossaga ko‘ra 2,3-qavslar U ga teng, 15-xossaga ko‘ra esa 1- va 4-qavslarning

o‘zlari qoladi. ko‘ra) = B
( A  B)  ( A  B) =(6-xossaga ko‘ra)= A  A  B =(13 va 14-xossalarga

Shunday qilib soddalashtirish natijasi quyidagicha:

(A ∪ B ∩ A) ∩ (A ∪ A ∩ B)  B