Pushing negations using DeMorgan — applying DeMorgan’s theorems to expressions with overbars (inversions) converts double and grouped inversions into equivalent forms with only single negations on single variables. Is this statement accurate?

Introduction / Context:
DeMorgan’s theorems are cornerstone identities in Boolean algebra used to manipulate logic expressions, especially when moving between NAND/NOR and AND/OR implementations. They “push” inversions inward so that negations apply directly to individual variables rather than to grouped sums or products.

Given Data / Assumptions:

• Operators: + for OR, · for AND, overbar/prime for NOT.
• Typical patterns: (X + Y)′ = X′ · Y′ and (X · Y)′ = X′ + Y′.
• Double inversions can be removed since (Z)′′ = Z.

Concept / Approach:
To eliminate group-level overbars, apply DeMorgan to replace a complemented sum with a product of complements or a complemented product with a sum of complements. After iterative application, any expression with complex nested overbars is transformed into an equivalent form where only variables carry the negation operator. This is especially useful when designing with NAND or NOR gates, since they naturally implement complemented sums/products.

Step-by-Step Solution:

Verification / Alternative check:
Build truth tables before and after transformation to confirm equality for all input combinations. Alternatively, implement both forms with gates and simulate; outputs match identically.

Why Other Options Are Wrong:

Common Pitfalls:
Forgetting to flip the operator (OR↔AND) when moving the bar; neglecting to complement every term inside the group; missing that double negation cancels.

Final Answer:
Accurate (Correct)