Boolean evaluation: which of the following Boolean OR expressions is incorrect under standard Boolean algebra rules (where 1 represents logic HIGH and “+” denotes OR)?
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A1 + 0 = 1
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B1 + 1 = 0
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C1 + 0 + 1 = 1
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D1 + 1 + 1 = 1
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ENone of the above
Answer
Correct Answer: 1 + 1 = 0
Explanation
Introduction / Context:Boolean algebra uses 1 and 0 to denote TRUE and FALSE (or HIGH and LOW). The OR operation (“+”) outputs 1 if any operand is 1. This question asks you to identify which expression violates the standard truth of OR.
Given Data / Assumptions:
- Use standard Boolean OR: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 1.
- Associativity allows grouping without changing results.
- We assume no XOR; “+” is strictly OR here.
Concept / Approach:Check each option against the OR truth rules. Any sum including a 1 must be 1, including 1 + 1 which equals 1, not 0. Multi-operand OR remains 1 if at least one operand is 1.
Step-by-Step Solution:
Evaluate 1 + 0: equals 1 → correct. Evaluate 1 + 1: equals 1 → the option stating 0 is incorrect. Evaluate 1 + 0 + 1: at least one 1 → equals 1 → correct. Evaluate 1 + 1 + 1: equals 1 → correct.Verification / Alternative check:Truth tables confirm 1 OR 1 = 1. No standard Boolean system makes 1 + 1 = 0; that result would correspond to XOR, not OR.
Why Other Options Are Wrong:
1 + 0 = 1: valid OR identity. 1 + 0 + 1 = 1 and 1 + 1 + 1 = 1: valid due to presence of 1s. None: invalid because there is indeed one incorrect expression (1 + 1 = 0).Common Pitfalls:Confusing OR with XOR; XOR of 1 and 1 is 0, but this question uses OR (+), not XOR (⊕).
Final Answer:1 + 1 = 0