2- amaliy mashg’ulot. Munosabatlar ustida

Munosabatlar kompozitsiyasiga doir topshiriqlar

A={a,b,c}, B={1,2,3}, C={α,β,γ} to‘plamlarda aniqlangan
^{R 1 A B} vа

R ₂  B  C
topilsin:
binаr munosаbаtlаrning kopаytmаsi yoki kompozitsiyasi

1.6.1.

R1={(a,3),(b,2),(c,1),(c,2)},

1.6.15.

R1={(a,3),(a,2),(a,1)},

	R2={(1,β),(2,α),(3,β), (3,γ)}		R2={(2,γ),(1,α),(1,β)}
1.6.2.	R1={(a,1),(a,3),(c,1),(c,3)}, R2={(2,α),(2,γ),(1,β), (3,α)}	1.6.16.	R1={(a,3),(a,2),(a,1)}, R2={(1,γ),(3,α),(1,β)}
1.6.3.	R1={(a,2),(b,1),(c,3)}, R2={(1,β),(2,β), (3,α)}	1.6.17.	R1={(a,3),(a,2),(a,1)}, R2={(1,γ),(1,α),(3,β)}
1.6.4.	R1={(a,3),(b,2),(c,1)}, R2={(1,γ),(2,α),(3,α)}	1.6.18.	R1={(a,3),(a,2),(a,1)}, R2={(3,γ),(2,α),(2,β)}
1.6.5.	R1={(a,2),(b,3),(c,1)}, R2={(1,γ),(2,β),(3,α)}	1.6.19.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(3,α),(2,β)}
1.6.6.	R1={(b,3),(b,2),(b,1)}, R2={(2,γ),(2,α),(2,β)}	1.6.20.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(2,α),(3,β)}
1.6.7.	R1={(a,1),(a,2),(a,3)}, R2={(3,γ),(3,α),(3,β)}	1.6.21.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(1,α),(1,β)}
1.6.8.	R1={(c,3),(c,2),(c,1)}, R2={(1,γ),(1,α),(2,β)}	1.6.22.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(1,α),(1,γ)}
1.6.9.	R1={(c,3),(c,2),(c,1)}, R2={(2,γ),(2,α),(2,β)}	1.6.23.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(1,α),(1,β)}
1.6.10.	R1={(c,3),(c,2),(c,1)}, R2={(3,γ),(3,α),(3,β)}	1.6.24.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(2,α),(2,β)}
1.6.11.	R1={(a,3),(a,2),(a,1)}, R2={(1,γ),(1,α),(1,β)}	1.6.25.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(2,α),(2,γ)}
1.6.12.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(2,α),(2,β)}	1.6.26.	R1={(b,3),(b,2),(b,1)}, R2={(2,β),(2,γ),(3,α)}
1.6.13.	R1={(b,3),(b,2),(b,1)}, R2={(1,γ),(1,α),(1,β)}	1.6.27.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(3,α),(2,γ)}
1.6.14.	R1={(b,3),(b,2),(b,1)}, R2={(3,γ),(3,α),(3,β)}	1.6.28.	R1={(b,3),(b,2),(b,1)}, R2={(1,β),(3,α),(3,γ)}
		1.6.29.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(3,γ),(2,β)}

1.3. Munosabatlar kompozitsiyasiga doir topshiriq(na’muna)

A={a,b,c}, B={1,2,3}, C={α,β,γ} to‘plamlarda aniqlangan
^{R 1 A B} vа

R ₂  B  C
topilsin:
binаr munosаbаtlаrning kopаytmаsi yoki kompozitsiyasi

1.6.0.

R1={(a,2),(a,3),(b,1),(c,2)}, R2={(1,α),(2,α),(2,β), (3,γ)}

1.3. Topshiriqning bajarilishi bo’yicha na’muna

1.6.0.
^{R 1 A B} vа
R ₂  B  C
binаr munosаbаtlаrning kopаytmаsi yoki

kompozitsiyasi,

R₁ ∘ R ₂  {( x, y): xA, yC ва zB topiladik i
kabi aniqlanadi, shunga ko‘ra:


(x, z) R ₁


va (z, y) R ₂}

^{R1 ∘ R 2 } {(a,2);(a,3);(b,1);(c,2)} {(1,α);(2,α);(2,β);(3,γ)}=
={(a,β);(a,α);(a,γ);(b,α);(c, α);(c, β)}


2-usul. R₁ va R₂ munosabatlarni quyidagicha chizmalarda ifodalab olamiz:


A to‘plam elementlarini B to‘plam elementlari orqali C to‘plam elementlari bilan bog‘lash mumkin bo‘lgan yo‘llarning uchlaridan iborat bo‘lgan to‘plamga R₁ va R₂ munosabatlarning kompozitsiyasini tashkil qiladi.