3. Мatematik mantiq asoslari. Mantiq funksiyalari uchun chinlik jadvalini tuzish
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3. Мatematik mantiq asoslari. 3.1. Mantiq funksiyalari uchun chinlik jadvalini tuzish
Quyidagi mantiq algebrasi funksiyalari uchun rostlik jadvallarini tuzing; 1.1 F(A,B,C)= A B (A C) 1.2 F(A,B,C)=C→( A B)
1.3 F(A,B,C)=A&B→ (A B)
1.4 F(A,B,C)=(A&B& C) ( A B) 1.5 F(A,B,C)=( A C) B 1.6 F(A,B,C)=(A→B)→ C
A→ B) (B→C) 1.8 F(A,B,C)=A (B→C) B 1.9 F(A,B,C)= (A&B
C)
1.10 F(A,B,C)=(A B)
( B C)
1.11 F(A,B,C)=( A→
C) B 1.12 F(A,B,C)=( B
C)→(A C) 1.13 F(A,B,C)=A→( B
C) 1.14
F(A,B,C)=( A→B) ( B→A) C 1.15 F(A,B,C)=C A
B 1.16
F(A,B,C)=A ( A B C) (A C) 1.17
F(A,B,C)=( A B) ( B A C) 1.18
F(A,B,C)=A (B A) ( A C)
1.19 F(A,B,C)=(A→B)&A& C
F(A,B,C)=( A&B)→(C&A) 1.21 F(A,B,C)=(A&B C)&A&
C 1.22 F(A,B,C)=(A&B A& B)&(C→B) 1.23 F(A,B,C)=(A B C A B C) A B 1.24 F(A,B,C)=(A→B)&(C→A) 1.25
F(A,B,C)=(A B&C A& C)&B 1.26 F(A,B,C)=(A B
C)→A C 1.27 F(A,B,C)=(A B)→(
C B A) 1.28 F(A,B,C)=(A→ B)
(C A) 1.29 F(A,B,C)=(A B)
( C B)
1.30 F(A,B,C)=((A B)
C)→A (( B C) (A C)
3.2. Rostlik jadvali bo‘yicha mantiq funksiyasi ko‘rinishini tiklash
B C F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10
F 11
F 12
F 13
F 14
F 15
0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1
16 F
F 18
F 19
F 20
F 21
F 22
F 23
F 24
F 25
F 26
F 27
F 28
F 29
F 30
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1
Mantiq qonunlari yordamida F(x,y,z) funksiyani soddalashtiring. 3.1 F(x,y,z)=( x
y z)&(x&y z)
3.2 F(x,y,z)=( x&y
z)&(x&z→y) 3.3 F(x,y,z)=(x y) (x&z (y→z)) 3.4 F(x,y,z)=(x y&z)
(( x y) z)
3.5 F(x,y,z)= (x→(y→z)) (x (y z)) 3.6 F(x,y,z)= (x
y z) (x→y
z)
3.7 F(x,y,z)=(x y
z) (x y z) ( (x y) z) 3.8 F(x,y,z)=((x→ y)
(x z)) (y z) 3.9 F(x,y,z)=(( x
y) (x y))→(z→
y)
3.10 F(x,y,z)= (
x→y) (((x→z) y) z) 3.11
F(x,y,z)= ((x y)→((x
y) y)) z 3.12 F(x,y,z)= ((x
y)→(
x z→y))→ x z 3.13 F(x,y,z)=((x y) z) x) y 3.14 F(x,y,z)=((x→y) (x→y
z))
(x y) 3.15
F(x,y,z)=(x→y) ((y→ z)→x
y)
3.16 F(x,y,z)=(x y)
( x→(y→z)) 3.17 F(x,y,z)=x→((y→z)→y z)
3.18 F(x,y,z)=(x (y→z))
(x y) 3.19
F(x,y,z)= (x y) (x z)) (x y z) 3.20 F(x,y,z)=( x
y) ((y z)→(x
x z)) 3.21
F(x,y,z)=(x y) ((y
z)→(x
z))
3.22 F(x,y,z)=x ((y
z) ( x→z)) 3.23 F(x,y,z)=(((x y)
z) y)&( y→z)
3.24 F(x,y,z)=((x y)
(y z)) (x (y→z)) 3.25
F(x,y,z)=(x y→z) ((x
y) z) 3.26
F(x,y,z)=(x y) (x x y y z (x y z)) 3.27
F(x,y,z)= (x y z) (x y x (y z) y& z) x 3.28 F((x,y,z)=((x y)→(x y))&((
x→y)→(x
y))
3.29 F(x,y,z)= ((x
y) (x z)) (x y z) 3.30 F(x,y,z)=((x y)
z→((x z) y))
((x
y) z) 3.4. Ikkilik mantiqiy elementlar
Quyidagi misollar uchun rele-kontakt sxemasi chizilib, sxema mantiq qonunlari asosida soddalashtirilsin:
4.1 F(x,y,z)=x&( x&y z)&(x
z)
4.2 F(x,y,z)=( x
y)&( y x&z)
4.3 F(x,y,z)=x&(y x)&(
x z) 4.4
F(x,y,z)=( x&y)→(z&x) 4.5 F(x,y,z)=(x&y z)&x&
z 4.6 F(x,y,z)= (x z x& y)&(z→y) 4.7
F(x,y,z)=(x y z x y&z)&x y 4.8 F(x,y,z)=(x& y&z x& z)&y 4.9
F(x,y,z)=( x y) ((y z)→(x x z)) 4.10
F(x,y,z)=(x y) ((y
z)→(x
z))
4.11 F(x,y,z)=x ((y
z) ( x→z)) 4.12 F(x,y,z)=(((x y)
z) y)&( y→z)
4.13 F(x,y,z)=((x y)
(y z)) (x (y→z)) 4.14
F(x,y,z)=(x y→z) ((x
y) z) 4.15 F(x,y,z)=(x y)
(x x y y z (x y z)) 4.16 F(x,y,z)= (x
y z) (x y x (y z) y& z) x 4.17
F((x,y,z)=((x y)→(x y))&((
x→y)→(x
y))
4.18 F(x,y,z)= ((x
y) (x z)) (x y z) 4.19 F(x,y,z)=((x y)
z→((x z) y))
((x
y) z) 4.20
F(x,y,z)=(( x y) (x y))→(z→ y)
4.21 F(x,y,z)= (
x→y) (((x→z) y) z) 4.22
F(x,y,z)= ((x y)→((x
y) y)) z 4.23 F(x,y,z)= ((x
y)→(
x z→y))→ x z 4.24 F(x,y,z)=((x y) z) x) y 4.25 F(x,y,z)=((x→y) (x→y
z))
(x y) 4.26
F(x,y,z)=(x→y) ((y→ z)→x
y)
4.27 F(x,y,z)=(x y)
( x→(y→z)) 4.28 F(x,y,z)=x→((y→z)→y z)
4.29 F(x,y,z)=(x (y→z))
(x y) 4.30
F(x,y,z)= (x y) (x z)) (x y z) 3.5. Karno kartalari
Quyidagi misollar uchun Karno kartalari tuzilsin, soddalashtirilsin, soddalashgan formulaga mos rele-kontakt sxemasi chizilsin: 5.1 F(0,0,0)=F(0,1,1)=F(1,1,0)=F(1,0,0)=1 5.2 F(0,0,0)=F(0,1,0)=F(1,1,0)=F(1,0,0)=1 5.3 F(0,0,1)=F(0,1,1)=F(1,1,1)=F(1,0,1)=1 5.4 F(0,0,1)=F(0,1,0)=F(1,1,0)=F(1,0,1)=1 5.5 F(0,0,0)=F(0,1,0)=F(1,1,1)=F(1,0,1)=1 5.6 F(0,0,0)=F(0,0,1)=F(1,0,0)=F(1,0,1)=1 5.7 F(0,1,0)=F(0,1,1)=F(1,1,0)=F(1,1,1)=1 5.8 F(0,0,0)=F(0,0,1)=F(0,1,0)=F(0,1,1)=1 5.9 F(0,0,0)=F(0,0,1)=F(1,1,0)=F(1,1,1)=1 5.10 F(1,1,0)=F(1,1,1)=F(1,0,0)=F(1,0,1)=1
5.11
F(0,1,0)=F(0,1,1)=F(1,0,0)=F(1,0,1)=1 5.12
F(0,1,0)=F(1,1,1)=F(1,0,0)=F(1,0,1)=1 5.13
F(0,1,0)=F(0,1,1)=F(1,1,1)=F(1,0,1)=1 5.14
F(0,1,1)=F(1,1,0)=F(1,1,1)=F(1,0,1)=1 5.15
F(0,0,0)=F(0,0,1)=F(0,1,0)=F(1,1,0)= F(1,0,0)=F(1,0,1)=1 5.16
F(0,0,0)=F(0,0,1)=F(0,1,1)=F(1,1,0)= F(1,0,0)=F(1,0,1)=1 5.17
F(0,0,0)=F(0,0,1)=F(1,1,0)=F(1,1,1)= F(1,0,0)=F(1,0,1)=1 5.18
F(0,0,0)=F(0,1,0)=F(0,1,1)=F(1,1,0)= F(1,1,1)=F(1,0,0)=1 5.19
F(0,0,0)=F(0,0,1)=F(0,1,0)=F(0,1,1)= F(1,1,0)=F(1,0,0)=1 5.20
F(0,0,0)=F(0,0,1)=F(0,1,0)=F(0,1,1)= F(1,1,0)=F(1,1,1)=1
5.21 F(0,0,0)=F(0,0,1)=F(0,1,0)=F(0,1,1)= F(1,0,0)=F(1,0,1)=1 5.22 F(0,1,0)=F(0,1,1)=F(1,1,0)=F(1,1,1)= F(1,0,0)=F(1,0,1)=1 5.23 F(0,0,0)=F(0,0,1)=F(0,1,0)=F(0,1,1)= F(1,1,0)=1 5.24 F(0,0,0)=F(0,1,0)=F(0,1,1)=F(1,1,0)= F(1,1,1)=1 5.25 F(0,0,0)=F(0,0,1)=F(0,1,0)=F(1,1,0)= F(1,0,0)=1 5.26 F(0,0,0)=F(0,1,0)=F(0,1,1)=F(1,1,0)= F(1,0,0)=1 5.27 F(0,0,0)=F(0,0,1)=F(0,1,0)=F(0,1,1)= F(1,1,0)=1 5.28 F(0,1,0,1)=F(0,1,1,1)=F(1,1,0,1)=F(1,1,1,1)=0 5.29 F(0,0,0,0)=F(0,0,1,0)=F(1,0,0,0)=F(1,0,1,0)=0 5.30 F(0,0,0,1)=F(0,0,1,1)=F(1,0,0,1)=F(1,0,1,1)=0 Download 356.99 Kb. Do'stlaringiz bilan baham: 
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