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.