GATE Exam > GATE Questions > (A + B)(A’ * B’) = ?a)1b)0c)ABd)A...
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(A + B)(A’ * B’) = ?
- a)1
- b)0
- c)AB
- d)AB’
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
(A + B)(A’ * B’) = ?a)1b)0c)ABd)AB’Correct answer is...
The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.
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(A + B)(A’ * B’) = ?a)1b)0c)ABd)AB’Correct answer is...
Understanding the Expression
To solve the expression \((A + B)(A' * B')\), we need to break it down using Boolean algebra rules.
Definitions of Terms
- A': The complement of A (not A).
- B': The complement of B (not B).
- A + B: The logical OR operation between A and B.
- A' * B': The logical AND operation between the complements of A and B.
Breaking Down the Expression
1. First Component: \(A + B\)
- This component will evaluate to true (1) if either A or B (or both) are true.
2. Second Component: \(A' * B'\)
- This component will evaluate to true (1) only if both A and B are false (0).
Combining the Components
Now, we need to analyze the overall expression \((A + B)(A' * B')\):
- The expression will be true (1) if both components are true.
- However, for \(A' * B'\) to be true, both A and B must be 0, which means \(A + B\) will be false (0).
Conclusion
- Therefore, the expression \((A + B)(A' * B')\) can never be true because:
- If \(A + B = 1\), then \(A' * B' = 0\).
- If \(A + B = 0\), then \(A' * B' = 1\) is true.
Thus, the entire expression evaluates to 0.
Final Answer
The correct answer is option b) 0.
To solve the expression \((A + B)(A' * B')\), we need to break it down using Boolean algebra rules.
Definitions of Terms
- A': The complement of A (not A).
- B': The complement of B (not B).
- A + B: The logical OR operation between A and B.
- A' * B': The logical AND operation between the complements of A and B.
Breaking Down the Expression
1. First Component: \(A + B\)
- This component will evaluate to true (1) if either A or B (or both) are true.
2. Second Component: \(A' * B'\)
- This component will evaluate to true (1) only if both A and B are false (0).
Combining the Components
Now, we need to analyze the overall expression \((A + B)(A' * B')\):
- The expression will be true (1) if both components are true.
- However, for \(A' * B'\) to be true, both A and B must be 0, which means \(A + B\) will be false (0).
Conclusion
- Therefore, the expression \((A + B)(A' * B')\) can never be true because:
- If \(A + B = 1\), then \(A' * B' = 0\).
- If \(A + B = 0\), then \(A' * B' = 1\) is true.
Thus, the entire expression evaluates to 0.
Final Answer
The correct answer is option b) 0.
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(A + B)(A’ * B’) = ?a)1b)0c)ABd)AB’Correct answer is option 'B'. Can you explain this answer?
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(A + B)(A’ * B’) = ?a)1b)0c)ABd)AB’Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about (A + B)(A’ * B’) = ?a)1b)0c)ABd)AB’Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (A + B)(A’ * B’) = ?a)1b)0c)ABd)AB’Correct answer is option 'B'. Can you explain this answer?.
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