1 Munosabatlar. Ekvivalent munosabatla
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1.5.26.
. 3 ; 4 , 2 ; 4 , 1 ; 4 , 2 ; 3 , 1 ; 3 , 3 ; 2 , 1 ; 2 , 4 ; 1 , 3 ; , 2 ; , 3 ; , 2 ; , 1 ; , 4 ; , 3 ; , 2 ; , 3 ; , 2 ; 2 1 R e e d d d b b b a a R
. 3 ; 4 , 2 ; 4 , 4 ; 3 , 1 ; 3 , 4 ; 2 , 1 ; 2 , 3 ; 1 , 2 ; 1 , 4 ; , 2 ; , 3 ; , 2 ; , 1 ; , 4 ; , 3 ; , 2 ; , 3 ; , 1 ; 2 1 R e e d d d b b b a a R
1.5.28. . 3 ; 4 , 4 ; 3 , 2 ; 3 , 1 ; 3 , 4 ; 2 , 3 ; 2 , 1 ; 2 , 2 ; 1 , 3 ; , 2 ; , 3 ; , 2 ; , 4 ; , 3 ; , 2 ; , 4 ; , 3 ; , 2 ; 2 1 R e e d d c c c a a a R
. 4 ; 4 , 3 ; 4 , 4 ; 3 , 2 ; 3 , 3 ; 2 , 1 ; 2 , 2 ; 1 , 1 ; 1 , 3 ; , 1 ; , 4 ; , 2 ; , 3 ; , 2 ; , 1 ; , 4 ; , 3 ; , 2 ; 2 1 R e e d d c c c a a a R
. 2 ; 4 , 1 ; 4 , 2 ; 3 , 1 ; 3 , 4 ; 2 , 2 ; 2 , 4 ; 1 , 3 ; 1 , 3 ; , 1 ; , 4 ; , 2 ; , 3 ; , 1 ; , 4 ; , 2 ; , 3 ; , 1 ; 2 1 R e e d d c c b b a a R
Na`muna: 1.5.0 - misolning ishlanishi
1) D l (R 1 )= {a, b. c, d, e} D l (R 2 )= {1, 2.3,4} D r (R 1 )= {1, 2. 3, 4} D r (R 2 )= {2. 3, 4} 2) Munosabat martitsalari:
R
,
1
0 0
0 0
1
1 0 1 1
1
0 1
1 0
0
,
0 0
0
1 1
1 1
0 0
1
0 1 0 1
1
0 0
1 0
1 2 R
, 2 2 2 2
R R
,
1101 1110 0110
0000 R
,
00010 11110 01010
10101 R
,
0001 0111 0111
0111 0001
0110 0111
0011 0001
0110 0111
0011 1 - 2 1 - 1 2 2
0001 0110 0110
0000 1101
1110 0110
0000 0001
0110 0111
0011 1 2 2 R R
3) 2
.
0001 0010 0100
1000
, 2 E bunda E R
2 R simmetrik emas, chunki
.
1 2 2
R
2 R antisimmetrik emas, chunki .
1 2 2
R R
2 R tranzitiv emas, chunki
.
2 2 2
R
1.6. Munosabatlar kompozitsiyasi. A={a,b,c}, B={1,2,3}, C={α,β,γ} to‘plamlarda aniqlangan B A R 1
C B R 2
munosаbаtlаrning kopаytmаsi yoki kompozitsiyasi topilsin:
R 1
R 2 ={(1,α),(2,α),(2,β), (3,γ)} 1.6.15. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(2,γ),(1,α),(1,β)} 1.6.1. R 1 ={(a,3),(b,2),(c,1),(c,2)}, R 2 ={(1,β),(2,α),(3,β), (3,γ)} 1.6.16. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(1,γ),(3,α),(1,β)} 1.6.2. R 1 ={(a,1),(a,3),(c,1),(c,3)}, R 2 ={(2,α),(2,γ),(1,β), (3,α)} 1.6.17. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(1,γ),(1,α),(3,β)} 1.6.3. R 1 ={(a,2),(b,1),(c,3)}, R 2 ={(1,β),(2,β), (3,α)} 1.6.18. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(3,γ),(2,α),(2,β)} 1.6.4. R 1 ={(a,3),(b,2),(c,1)}, R 2 ={(1,γ),(2,α),(3,α)} 1.6.19. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(2,γ),(3,α),(2,β)} 1.6.5. R 1 ={(a,2),(b,3),(c,1)}, R 2 ={(1,γ),(2,β),(3,α)} 1.6.20. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(2,γ),(2,α),(3,β)} 1.6.6. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(2,γ),(2,α),(2,β)} 1.6.21. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(1,α),(1,β)} 1.6.7. R 1 ={(a,1),(a,2),(a,3)}, R 2 ={(3,γ),(3,α),(3,β)} 1.6.22. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(1,α),(1,γ)} 1.6.8. R 1 ={(c,3),(c,2),(c,1)}, R 2 ={(1,γ),(1,α),(2,β)} 1.6.23. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(1,α),(1,β)} 1.6.9. R 1 ={(c,3),(c,2),(c,1)}, R 2 ={(2,γ),(2,α),(2,β)} 1.6.24. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(2,α),(2,β)} 1.6.10. R 1 ={(c,3),(c,2),(c,1)}, R 2 ={(3,γ),(3,α),(3,β)} 1.6.25. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(2,α),(2,γ)} 1.6.11. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(1,γ),(1,α),(1,β)} 1.6.26. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(2,β),(2,γ),(3,α)} 1.6.12. R 1 ={(a,3),(a,2),(a,1)}, R 2 ={(2,γ),(2,α),(2,β)} 1.6.27. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(3,α),(2,γ)} 1.6.13. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(1,γ),(1,α),(1,β)} 1.6.28. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(1,β),(3,α),(3,γ)} 1.6.14. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,γ),(3,α),(3,β)} 1.6.29. R 1 ={(b,3),(b,2),(b,1)}, R 2 ={(3,β),(3,γ),(2,β)}
0-topshiriqning ishlanishi. 1.6.0. B A R 1
C B R 2
} R
(z,
va
R z)
(x,
i topiladik B z
ва C y A, x : ) y , {(
2
1 2
1
x R R
kabi aniqlanadi, shunga ko‘ra: 2 1
R R {(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)}
1.7. Munosabatlarni funktsiyaga tekshiring: A={1,2,3,4}, B={a,b,c,d} to‘plamlar dekart ko‘paytmasida aniqlangan quyidagicha R munosabatlar funksiya bo‘ladimi? Agar bo‘lsa in’yektiv, syur’yektiv, biyektiv funksiya bo‘ladimi? 1.7.0. R={(1,a),(1,b),(2,a),(3,d)} 1.7.15. R={(3,b),(2,a),(1,c),(4,d)} 1.7.1. R={(1,a),(2,b),(3,a),(4,d)} 1.7.16. R={(4,c),(3,b),(3,a),(4,d)} 1.7.2. R={(1,a),(2,c),(3,b),(3,d)} 1.7.17. R={(4,a),(1,b),(2,a),(3,c)} 1.7.3. R={(2,a),(1,b),(2,c),(4,d)} 1.7.18. R={(3,b),(2,c),(1,a),(4,d)} 1.7.4. R={(1,a),(2,b),(3,c),(4,d)} 1.7.19. R={(2,a),(3,b),(4,b),(3,a)} 1.7.5. R={(2,a),(1,b),(3,d),(4,c)} 1.7.20. R={(1,a),(2,b),(3,a),(4,d)} 1.7.6. R={(1,b),(2,c),(3,c),(4,d)} 1.7.21. R={(4,c),(2,a),(3,a),(3,d)} 1.7.7. R={(4,a),(3,b),(2,a),(3,c)} 1.7.22. R={(3,a),(1,b),(2,c)} 1.7.8. R={(3,a),(1,b),(2,a),(4,d)} 1.7.23. R={(2,a),(1,b),(4,c),(3,d)} 1.7.9. R={(1,a),(4,b),(2,d),(3,c)} 1.7.24. R={(4,b),(1,c),(2,d),(3,c)} 1.7.10. R={(4,d),(1,b),(2,c),(3,a)} 1.7.25. R={(2,a),(1,b),(3,c),(4,d)} 1.7.11. R={(1,a),(2,b),(3,c),(4,b)} 1.7.26. R={(2,b),(3,a),(4,c),(1,d)} 1.7.12. R={(3,a),(4,b),(2,d),(3,c)} 1.7.27. R={(4,c),(2,b),(3,a),(1,d)} 1.7.13. R={(4,b),(3,a),(2,c),(3,d)} 1.7.28. R={(3,a),(2,b),(4,a),(1,c)} 1.7.14. R={(4,a),(1,b),(2,d),(3,c)} 1.7.29. R={(4,a),(1,b),(2,c),(3,d)}
Na’muna: 1.7.0. A={1,2,3,4}, B={a,b,c,d} to‘plamlar dekart ko‘paytmasida aniqlangan R={(1,a),(1,b),(2,a),(3,d)} munosabat funktsiya bo‘ladimi? Agar bo‘lsa in’yektiv, syur’yektiv, biyektiv funksiya bo‘ladimi? R
1) A R D l ) ( ,
B
) ( f D r , 2) R x
) y
, ( 1 , R x
) y
, ( 2 ekanligidan 2 1
y ekanligi kelib chiqsa R munosabatga A to‘plamdan B to‘plamga funktsiya yoki akslantirish bo‘ladi, shunga ko‘ra: 1) D
l (R)={1,2,3} A, D
r (R)={a,b,d} B;
2) (1,a) R, (1,b) R ekanligidan a=b ekanligi kelib chiqishi lozim edi, lekin a
esa ushbu elementlar alohida-alohida berilgan. Demak R munosabat funksiya bo‘la olmaydi.
Quyidagicha aniqlangan f i (x):(-∞;+∞)→(-∞;+∞) funksiyalar in‘yektivlik, syur’yektivlik, biyektivlikka tekshirilsin: 1.8.0. f 1 (x)=x 2 1.8.1. f 2 (x)=lnx 1.8.2. f 3 (x)=x*sinx 1.8.3. f 4 (x)=tgx 1.8.4. f 5 (x)=2x+1 1.8.5. f 6 (x)=sinx 1.8.6. f 7 (x)=cosx 1.8.7. f 8 (x)=ctgx 1.8.8. f 9 (x)=a x
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