Properties of NAND
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Theorem
Let $\uparrow$ signify the NAND operation.
The following results hold:
NAND with Equal Arguments
- $p \uparrow p \dashv \vdash \neg p$
That is, the NAND of a proposition with itself corresponds to the negation operation.
NAND is Commutative
- $p \uparrow q \dashv \vdash q \uparrow p$
NAND is not Associative
- $p \uparrow \paren {q \uparrow r} \not \vdash \paren {p \uparrow q} \uparrow r$