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
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B
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C
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A&B
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⌐ (A&B)
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A\/B
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A\/B~C
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α(A, B, C)= ⌐(A&B)→(A\/B~C)
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0
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0
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0
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0
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1
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0
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1
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1
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1
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1
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0
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0
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0
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0
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1
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0
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0
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1
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1
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0
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0
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0
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1
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1
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0
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1
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1
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1
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1
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1
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0
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0
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0
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1
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1
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0
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0
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1
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0
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1
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0
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1
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1
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1
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1
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1
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1
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0
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1
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0
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1
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0
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1
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1
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1
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1
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1
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0
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1
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1
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1
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Quyidagi mantiq algebrasi funksiyalari uchun rostlik jadvallarini tuzing;
F(A,B,C)= AB(AC)
F(A,B,C)=C→(AB)
F(A,B,C)=A&B→(AB)
F(A,B,C)=(A&B&C)(A B)
F(A,B,C)=(AC)B
F(A,B,C)=(A→B)→C
F(A,B,C)=(A→B)(B→C)
F(A,B,C)=A(B→C)B
F(A,B,C)=(A&BC)
F(A,B,C)=(AB)(BC)
F(A,B,C)=(A→C)B
F(A,B,C)=(BC)→(AC)
F(A,B,C)=A→(BC)
F(A,B,C)=(A→B)(B→A)C
F(A,B,C)=CAB
F(A,B,C)=A(ABC)(AC)
F(A,B,C)=(AB)(BAC)
F(A,B,C)=A(BA)(AC)
F(A,B,C)=(A→B)&A&C
F(A,B,C)=(A&B)→(C&A)
F(A,B,C)=(A&BC)&A&C
F(A,B,C)=(A&BA&B)&(C→B)
F(A,B,C)=(AB CABC)AB
F(A,B,C)=(A→B)&(C→A)
F(A,B,C)=(AB&CA&C)&B
F(A,B,C)=(ABC)→AC
F(A,B,C)=(AB)→(CBA)
F(A,B,C)=(A→B)(CA)
F(A,B,C)=(AB)(CB)
F(A,B,C)=((AB)C)→A((BC)(AC)
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