NTA UGC NET Aug 2024 Paper-2
March 25, 2025KVS DEC-2017
March 26, 2025GATE-2024-CS1(Forenoon)
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Question 47
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Consider a Boolean expression given by F(X,Y,Z) = Σ(3,5,6,7).
Which of the following statements is/are CORRECT?
Which of the following statements is/are CORRECT?
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F(X,Y,Z)=Π(0,1,2,4)
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F(X,Y,Z)=XY+YZ+XZ
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F(X,Y,Z) is independent of input Y
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F(X,Y,Z) is independent of input X
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Question 47 Explanation:
(A) F(X, Y, Z) = Π(0, 1, 2, 4)
This statement represents the product of terms (AND operation) for the minterms (0, 1, 2, 4). However, the actual expression uses the sum of terms (OR operation) denoted by Σ.
Here’s the key point: The given minterms (3, 5, 6, 7) can be interpreted in two ways:
Standard Interpretation (Sum of Terms): This is the more common interpretation, where the expression represents the OR operation of the minterms. In this case, the statement (A) would be incorrect.
Less Common Interpretation (Negation of Product of Terms): In some contexts, a Boolean expression can be written as the negation of its complement. The complement of F(X, Y, Z) would be the product of terms for all combinations where the output is 0 (maxterms). In this specific case, the maxterms would be (0, 1, 2, 4). Taking the negation (NOT operation) of the complement would result in the original expression F(X, Y, Z). So, under this less common interpretation, statement (A) could be considered correct.
(B) F(X, Y, Z) = XY + YZ + XZ
This statement represents an OR operation (sum of terms) using product of variables (XY, YZ, XZ). However, these specific terms don’t directly correspond to the minterms (3, 5, 6, 7).
This statement represents the product of terms (AND operation) for the minterms (0, 1, 2, 4). However, the actual expression uses the sum of terms (OR operation) denoted by Σ.
Here’s the key point: The given minterms (3, 5, 6, 7) can be interpreted in two ways:
Standard Interpretation (Sum of Terms): This is the more common interpretation, where the expression represents the OR operation of the minterms. In this case, the statement (A) would be incorrect.
Less Common Interpretation (Negation of Product of Terms): In some contexts, a Boolean expression can be written as the negation of its complement. The complement of F(X, Y, Z) would be the product of terms for all combinations where the output is 0 (maxterms). In this specific case, the maxterms would be (0, 1, 2, 4). Taking the negation (NOT operation) of the complement would result in the original expression F(X, Y, Z). So, under this less common interpretation, statement (A) could be considered correct.
(B) F(X, Y, Z) = XY + YZ + XZ
This statement represents an OR operation (sum of terms) using product of variables (XY, YZ, XZ). However, these specific terms don’t directly correspond to the minterms (3, 5, 6, 7).
Correct Answer: B
Question 47 Explanation:
(A) F(X, Y, Z) = Π(0, 1, 2, 4)
This statement represents the product of terms (AND operation) for the minterms (0, 1, 2, 4). However, the actual expression uses the sum of terms (OR operation) denoted by Σ.
Here’s the key point: The given minterms (3, 5, 6, 7) can be interpreted in two ways:
Standard Interpretation (Sum of Terms): This is the more common interpretation, where the expression represents the OR operation of the minterms. In this case, the statement (A) would be incorrect.
Less Common Interpretation (Negation of Product of Terms): In some contexts, a Boolean expression can be written as the negation of its complement. The complement of F(X, Y, Z) would be the product of terms for all combinations where the output is 0 (maxterms). In this specific case, the maxterms would be (0, 1, 2, 4). Taking the negation (NOT operation) of the complement would result in the original expression F(X, Y, Z). So, under this less common interpretation, statement (A) could be considered correct.
(B) F(X, Y, Z) = XY + YZ + XZ
This statement represents an OR operation (sum of terms) using product of variables (XY, YZ, XZ). However, these specific terms don’t directly correspond to the minterms (3, 5, 6, 7).
This statement represents the product of terms (AND operation) for the minterms (0, 1, 2, 4). However, the actual expression uses the sum of terms (OR operation) denoted by Σ.
Here’s the key point: The given minterms (3, 5, 6, 7) can be interpreted in two ways:
Standard Interpretation (Sum of Terms): This is the more common interpretation, where the expression represents the OR operation of the minterms. In this case, the statement (A) would be incorrect.
Less Common Interpretation (Negation of Product of Terms): In some contexts, a Boolean expression can be written as the negation of its complement. The complement of F(X, Y, Z) would be the product of terms for all combinations where the output is 0 (maxterms). In this specific case, the maxterms would be (0, 1, 2, 4). Taking the negation (NOT operation) of the complement would result in the original expression F(X, Y, Z). So, under this less common interpretation, statement (A) could be considered correct.
(B) F(X, Y, Z) = XY + YZ + XZ
This statement represents an OR operation (sum of terms) using product of variables (XY, YZ, XZ). However, these specific terms don’t directly correspond to the minterms (3, 5, 6, 7).