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Boolean Addition and Complement

Given the following statementsStatement 1:Addition in Boolean algebra is equivalent to the NOR function.Statement 2:“The complement of a product of variables is equal to the sum of the complements of each variable” is a statement of DeMorgan’s theorem.Choose the correct option for the above statements
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Answer & Explanation
Correct AnswerC. Statement 1 is false, but statement 2 is true

Quick Explanation

Boolean addition corresponds to OR, not NOR, so statement 1 is false. DeMorgan’s theorem states that the complement of a product equals the sum of the complements, (XY)̄=X̄+Ȳ, so statement 2 is true. Hence option C.

Formula / Key Relation

(XY)̄=X̄+Ȳ; X+Y = OR
Boolean Addition and Complement explanatory diagram

Detailed Explanation

Correct Answer

C — Statement 1 is false, but statement 2 is true

Concept and Reasoning

Boolean addition corresponds to OR, not NOR, so statement 1 is false. DeMorgan’s theorem states that the complement of a product equals the sum of the complements, (XY)̄=X̄+Ȳ, so statement 2 is true. Hence option C.

Calculation / Key Relation

(XY)̄=X̄+Ȳ

X+Y = OR

Exam Takeaway

Boolean “+” means OR; a bar over OR gives NOR.

Common Mistake

Do not interpret Boolean addition as ordinary arithmetic addition.

Quick Trick

Boolean “+” means OR; a bar over OR gives NOR.

Common Mistake

Do not interpret Boolean addition as ordinary arithmetic addition.

Exam Tip

Boolean “+” means OR; a bar over OR gives NOR.

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