Properties of NOR

Theorem

Let $\downarrow$ signify the NOR operation.

The following results hold:

NOR With Equal Arguments

$p \downarrow p \dashv \vdash \neg p$

That is, the NOR of a proposition with itself corresponds to the negation operator.

NOR is Commutative

$p \downarrow q \dashv \vdash q \downarrow p$

NOR is Not Associative

$p \downarrow \left({q \downarrow r}\right) \not \vdash \left({p \downarrow q}\right) \downarrow r$