Question
Download Solution PDFबूलियन फलन AB + AC ______ के समकक्ष है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
बुलियन बीजगणित के महत्वपूर्ण अभिगृहीत और डी मॉर्गन के नियम:
- दोहरा व्युत्क्रमण
- A . A = A
- A .
- A + 1 = 1
- A + A = A
- A +
डी मॉर्गन के नियम:
नियम 1:
नियम 2:
गणना:
माना कि दिया गया फलन Y है
Y = AB + AC
अबबूलियन बीजगणित के महत्वपूर्ण गुणों का उपयोग करके विस्तार करते हुए:
Y = AB(C + C̅) + AC(B + B̅)
Y = ABC + ABC̅ + ACB + ACB̅
चूँकि ABC + ACB = ABC
Y = ABC + ABC̅ + ACB̅
Y निम्न रूप में भी लिखा जा सकता है:
Y = ABC + ABC' + AB'C
इसलिए विकल्प (4) सही उत्तर है।
Important Points
|
नाम |
AND रूप |
OR रूप |
|
तत्समक का नियम |
1.A = A |
0 + A = A |
|
शून्य का नियम |
0.A = 0 |
1 + A = 1 |
|
वर्गसम का नियम |
A.A = A |
A + A = A |
|
व्युत्क्रम का नियम |
AA’ = 0 |
A + A’ = 1 |
|
क्रम-विनिमय नियम |
AB = BA |
A + B = B + A |
|
साहचर्य नियम |
(AB)C |
(A + B) + C = A + (B + C) |
|
वितरक नियम |
A + BC = (A + B)(A + C) |
A(B + C) = AB + AC |
|
अवशोषण नियम |
A(A + B) = A |
A + AB = A |
|
डी मॉर्गन का नियम |
(AB)’ = A’ + B’ |
(A + B)’ = A’B’ |
Last updated on Jul 18, 2025
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