Muhammad al-xorazmiy nomidagi toshkent axborot texnologiyalari universiteti kompyuter injiniringi fakulteti kompyuter tizimlari kafedrasi

1.4. Mantiq funksiyalari uchun chinlik jadvalini tuzish

Ta’rif 1. α formulaning barcha mantiqiy imkoniyatlari va bu mantiqiy imkoniyatlardagi α formulaning qiymatlari keltirilgan jadvaliga rostlik (chinlik) jadvali deyiladi.
Masalan α(A, B, C)= ⌐(A&B)→(A\/B~C) formulaning rostlik jadvalini topish uchun, amallar bajarilish ketma-ketligi:

1) qavs ichidagi amal 2) ⌐ 3) & 4) \/ 5) ~ → e’tiborga olinib birin-ketin amallar bajariladi va formulaning rostlik jadvali topiladi.

A	B	C	A&B	⌐ (A&B)	A\/B	A\/B~C	α(A, B, C)= ⌐(A&B)→(A\/B~C)
0	0	0	0	1	0	1	1
0	0	1	0	1	0	0	0
0	1	0	0	1	1	0	0
0	1	1	0	1	1	1	1
1	0	0	0	1	1	0	0
1	0	1	0	1	1	1	1
1	1	0	1	0	1	0	1
1	1	1	1	0	1	1	1

Quyidagi mantiq algebrasi funksiyalari uchun rostlik jadvallarini tuzing;

1. F(A,B,C)= AB(AC)

   
   

2. F(A,B,C)=C→(AB)

   
   

3. F(A,B,C)=A&B→(AB)

   
   

4. F(A,B,C)=(A&B&C)(A B)

   
   

5. F(A,B,C)=(AC)B

   
   

6. F(A,B,C)=(A→B)→C

   
   

7. F(A,B,C)=(A→B)(B→C)

   
   

8. F(A,B,C)=A(B→C)B

   
   

9. F(A,B,C)=(A&BC)

   
   

10. F(A,B,C)=(AB)(BC)

    
    

11. F(A,B,C)=(A→C)B

    
    

12. F(A,B,C)=(BC)→(AC)

    
    

13. F(A,B,C)=A→(BC)

    
    

14. F(A,B,C)=(A→B)(B→A)C

    
    

15. F(A,B,C)=CAB

    
    

16. F(A,B,C)=A(ABC)(AC)

    
    

17. F(A,B,C)=(AB)(BAC)

    
    

18. F(A,B,C)=A(BA)(AC)

    
    

19. F(A,B,C)=(A→B)&A&C

    
    

20. F(A,B,C)=(A&B)→(C&A)

    
    

21. F(A,B,C)=(A&BC)&A&C

    
    

22. F(A,B,C)=(A&BA&B)&(C→B)

    
    

23. F(A,B,C)=(AB CABC)AB

    
    

24. F(A,B,C)=(A→B)&(C→A)

    
    

25. F(A,B,C)=(AB&CA&C)&B

    
    

26. F(A,B,C)=(ABC)→AC

    
    

27. F(A,B,C)=(AB)→(CBA)

    
    

28. F(A,B,C)=(A→B)(CA)

    
    

29. F(A,B,C)=(AB)(CB)

    
    

30. F(A,B,C)=((AB)C)→A((BC)(AC)

    
    

Xulosa
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