Munosabatlar ustida amallar. Munosabatlar kompozitsiyasi. Binar munosabatlar va ularning matrisalarini toppish (4 soat) Reja

2.2. Topshiriqning bajarilisi bo’yicha na’muna

1) D_l(R₁)= {a, b. c, d, e} D_l(R₂)= {1, 2.3,4}

D_r(R₁)= {1, 2. 3, 4} D_r(R₂)= {2. 3, 4}
2) Munosabat martitsalari:






3) refleksiv emas, chunki
simmetrik emas, chunki
antisimmetrik emas, chunki
tranzitiv emas, chunki


2.3. Munosabatlar kompozitsiyasiga doir topshiriqlar
A={a,b,c}, B={1,2,3}, C={α,β,γ} to‘plamlarda aniqlangan vа binаr munosаbаtlаrning kopаytmаsi yoki kompozitsiyasi topilsin:

2.3.1.	R1={(a,3),(b,2),(c,1),(c,2)}, R2={(1,β),(2,α),(3,β), (3,γ)}	2.3.15.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(1,α),(1,β)}
2.3.2.	R1={(a,1),(a,3),(c,1),(c,3)}, R2={(2,α),(2,γ),(1,β), (3,α)}	2.3.16.	R1={(a,3),(a,2),(a,1)}, R2={(1,γ),(3,α),(1,β)}
2.3.3.	R1={(a,2),(b,1),(c,3)}, R2={(1,β),(2,β), (3,α)}	2.3.17.	R1={(a,3),(a,2),(a,1)}, R2={(1,γ),(1,α),(3,β)}
2.3.4.	R1={(a,3),(b,2),(c,1)}, R2={(1,γ),(2,α),(3,α)}	2.3.18.	R1={(a,3),(a,2),(a,1)}, R2={(3,γ),(2,α),(2,β)}
2.3.5.	R1={(a,2),(b,3),(c,1)}, R2={(1,γ),(2,β),(3,α)}	2.3.19.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(3,α),(2,β)}
2.3.6.	R1={(b,3),(b,2),(b,1)}, R2={(2,γ),(2,α),(2,β)}	2.3.20.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(2,α),(3,β)}
2.3.7.	R1={(a,1),(a,2),(a,3)}, R2={(3,γ),(3,α),(3,β)}	2.3.21.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(1,α),(1,β)}
2.3.8.	R1={(c,3),(c,2),(c,1)}, R2={(1,γ),(1,α),(2,β)}	2.3.22.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(1,α),(1,γ)}
2.3.9.	R1={(c,3),(c,2),(c,1)}, R2={(2,γ),(2,α),(2,β)}	2.3.23.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(1,α),(1,β)}
2.3.10.	R1={(c,3),(c,2),(c,1)}, R2={(3,γ),(3,α),(3,β)}	2.3.24.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(2,α),(2,β)}
2.3.11.	R1={(a,3),(a,2),(a,1)}, R2={(1,γ),(1,α),(1,β)}	2.3.25.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(2,α),(2,γ)}
2.3.12.	R1={(a,3),(a,2),(a,1)}, R2={(2,γ),(2,α),(2,β)}	2.3.26.	R1={(b,3),(b,2),(b,1)}, R2={(2,β),(2,γ),(3,α)}
2.3.13.	R1={(b,3),(b,2),(b,1)}, R2={(1,γ),(1,α),(1,β)}	2.3.27.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(3,α),(2,γ)}
2.3.14.	R1={(b,3),(b,2),(b,1)}, R2={(3,γ),(3,α),(3,β)}	2.3.28.	R1={(b,3),(b,2),(b,1)}, R2={(1,β),(3,α),(3,γ)}
		2.3.29.	R1={(b,3),(b,2),(b,1)}, R2={(3,β),(3,γ),(2,β)}

2.3. Munosabatlar kompozitsiyasiga doir topshiriq(na’muna)

A={a,b,c}, B={1,2,3}, C={α,β,γ} to‘plamlarda aniqlangan vа binаr munosаbаtlаrning kopаytmаsi yoki kompozitsiyasi topilsin:

1.6.0.

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

2.3. Topshiriqning bajarilishi bo’yicha na’muna
1.6.0. vа binаr munosаbаtlаrning kopаytmаsi yoki kompozitsiyasi,
kabi aniqlanadi, shunga ko‘ra:
{(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.