Normal shakllar. Mukammal normal shakllar. Rostlik jadvali bo‘yicha mantiq funksiyalarining ko‘rinishini tiklash(2 soat). Reja

Misol 2. formulani DNSh ga keltiramiz.





– MDNSh.
Misol 3. formulani MDNSh ga keltiramiz.





– mDNSh.
Xuddi shuningdek, ixtiyoriy formulani MKNSh ga keltirish mumkin.
Nazorat uchun savollar:

1. 
   Mantiq formulasi ko‘rinishi 0 ga teng qiymatlari bo‘yicha qanday tiklanadi?
   
2. 
   Mantiq formulasi ko‘rinishi 1 ga teng qiymatlari bo‘yicha qanday tiklanadi?
   

3. 
   Tavtologiya va ziddiyat formulalari uchun MKNSh va MDNSh haqidagi teoremalarni ayting.
   
4. 
   Jegalkin polinomi ta’rifini ayting. Misol keltiring.
   
5. 
   Jegalkin ko’phadi darajasi deganda nimani tushunasiz?
   
6. 
   Bul ko’phadlari bilan Jegalkin ko’phadining farqi nimada?
   

Mustaqil yechish uchun masalalar:
Quyidagi Bul formulalarini Jegalkin polinomiga o’tkazing:

1. 
   α(A,B,C)= AB(AC)
   
2. 
   α (A,B,C)=C→(AB)
   
3. 
   α (A,B,C)=A&B→(AB)
   
4. 
   α (A,B,C)=(A&B&C)(A B)
   
5. 
   α (A,B,C)=(AC)B
   
6. 
   α (A,B,C)=(A→B)→C
   
7. 
   α (A,B,C)=(A→B)(B→C)
   
8. 
   α (A,B,C)=A(B→C)B
   
9. 
   α (A,B,C)=(A&BC)
   
10. 
    α(A,B,C)=(AB)(BC)
    
11. 
    α(A,B,C)=(A→C)B
    
12. 
    α (A,B,C)=A→(BC)
    
13. 
    α(A,B,C)=(A→B)(B→A)C
    
14. 
    α(A,B,C)=CAB
    
15. 
    α(A,B,C)=A(ABC)(AC)
    
16. 
    α(A,B,C)=(AB)(BAC)
    
17. 
    α(A,B,C)=A(BA)(AC)