Properties of NAND

From ProofWiki
Jump to navigation Jump to search

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

$p \uparrow \paren {q \uparrow r} \not \vdash \paren {p \uparrow q} \uparrow r$