## Logical Graphs, Truth Tables, Venn Diagrams • 7

On the subject of Peirce’s ampheck operators, see the earlier discussion of their duality under entitative and existential interpretations.

The ampheck operators are dual with respect to entitative and existential interpretations:

• $f_{1} = f_{0001} = \text{both not} : \mathbb{B} \times \mathbb{B} \to \mathbb{B}$
• $f_{7} = f_{0111} = \text{not both} : \mathbb{B} \times \mathbb{B} \to \mathbb{B}$

Under the existential interpretation:

• $f_{1} = f_{0001} = \text{both not} = \texttt{(} x \texttt{)(} y \texttt{)}$
• $f_{7} = f_{0111} = \text{not both} = \texttt{(} xy \texttt{)}$

Under the entitative interpretation:

• $f_{1} = f_{0001} = \text{both not} = \texttt{(} xy \texttt{)}$
• $f_{7} = f_{0111} = \text{not both} = \texttt{(} x \texttt{)(} y \texttt{)}$

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