Functionally Complete Logical Connectives/NOR

From ProofWiki
Jump to navigation Jump to search


The singleton set containing the following logical connective:

$\set \downarrow$: NOR

is functionally complete.


From Functionally Complete Logical Connectives: Negation and Disjunction, any boolean expression can be expressed in terms of $\lor$ and $\neg$.

From NOR with Equal Arguments:

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

From Disjunction in terms of NOR:

$p \lor q \dashv \vdash \paren {p \downarrow q} \downarrow \paren {p \downarrow q}$

demonstrating that $p \lor q$ can be represented solely in terms of $\downarrow$.

That is, $\set \downarrow$ is functionally complete.


Also see