Gate equivalence by bubble movement: The observation that a bubbled-input OR gate performs the same logic function as a bubbled-output AND gate is known as what?

Introduction / Context:
Bubble notation captures logical inversion on gate inputs and outputs. DeMorgan’s theorems formalize how inversions move across AND/OR gates while swapping the gate type, a powerful technique for designing with NAND/NOR-only libraries and for reading schematics quickly.

Given Data / Assumptions:

• Bubbled input: inverted input variable to a gate.
• Bubbled output: inverted output of a gate.
• Goal: name the principle equating bubbled-input OR to bubbled-output AND.

Concept / Approach:
DeMorgan’s second theorem states (A + B)' = A' • B'. Interpreted in gate form, an OR with both inputs inverted (bubbled-input OR) yields the same function as an AND with an inverted output (bubbled-output AND), i.e., NOR ≡ AND-with-inverted-inputs and equally NAND ≡ OR-with-inverted-inputs depending on the specific form used.

Step-by-Step Solution:
Start with Y = (A + B)'.Apply DeMorgan: Y = A' • B'.Map to gates: left side is an OR with output bubble (NOR) or equivalently an OR with bubbled inputs feeding an AND.Thus, a bubbled-input OR and a bubbled-output AND implement the same logic.

Verification / Alternative check:
Truth tables or logic-simulation confirm functional identity. Schematic re-drawing with bubble-pushing gives identical simplified forms.

Why Other Options Are Wrong:
Karnaugh map: a minimization tool, not a law.Commutative / associative laws: reorder or regroup operations; they do not involve inversion movement.

Common Pitfalls:
Confusing input versus output bubbles. DeMorgan requires flipping the gate type while inverting all lines that cross the inversion boundary.

Final Answer:
DeMorgan's second theorem