## Animated Logical Graphs • 75

Re: Richard J. LiptonThe Art Of Math
Re: Animated Logical Graphs • (30)(45)(57)(58)(59)(60)(61)(62)(63)(64)(65)(66)(69)(70)(71)(72)(73)(74)

Continuing our scan of the Table in Episode 72, the next two orbits contain the logical graphs for the boolean functions $f_{2}, f_{11}, f_{4}, f_{13},$ in that order.  A first glance shows these two orbits have surprisingly intricate structures and relationships to each other — let’s isolate that section for a closer look.

$\text{Peirce Duality} \stackrel{_\bullet}{} \text{Subtractions and Implications}$

• The boolean functions $f_{2}$ and $f_{4}$ are called subtraction functions.
• The boolean functions $f_{11}$ and $f_{13}$ are called implication functions.
• The logical graphs for $f_{2}$ and $f_{11}$ are dual to each other.
• The logical graphs for $f_{4}$ and $f_{13}$ are dual to each other.

The values of the subtraction and implication functions for each $(x, y) \in \mathbb{B} \times \mathbb{B}$ and the text expressions for their logical graphs are given in the following Table.

### Resources

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
cc: Structural Modeling (1) (2) • Systems Science (1) (2)
cc: Cybernetics (1) (2) • Ontolog Forum (1) (2)
cc: FB | Logical GraphsLaws of Form

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