Question:
A three-variable function \((A \oplus B \oplus C)’ = \text{ ?}\)
तीन चर वाला फलन \((A \oplus B \oplus C)’ = \text{ ?}\)
Options:
- \((A \odot B \odot C)’\)
- \(A \oplus B \odot C’\)
- \(A \odot B \oplus C\)
- \(A \oplus B \odot C\)
- \((A \odot B \odot C)’\)
- \(A \oplus B \odot C’\)
- \(A \odot B \oplus C\)
- \(A \oplus B \odot C\)
Correct Answer: d)
Explanation:
In Boolean logic, the complement of the XOR of two expressions is the XNOR operation: \((X \oplus Y)’ = X \odot Y\).
Grouping the first two variables \(X = (A \oplus B)\) and \(Y = C\):
\[ ((A \oplus B) \oplus C)’ = (A \oplus B) \odot C = A \oplus B \odot C \]
Hence, \((A \oplus B \oplus C)’ = A \oplus B \odot C\).
बूलियन तर्क में, दो व्यंजकों के XOR का पूरक (complement) XNOR ऑपरेशन होता है: \((X \oplus Y)’ = X \odot Y\)।
यहाँ \(X = (A \oplus B)\) और \(Y = C\) मानने पर:
\[ ((A \oplus B) \oplus C)’ = (A \oplus B) \odot C = A \oplus B \odot C \]
अतः सही उत्तर \(A \oplus B \odot C\) है।