```On Thu, 16 Mar 2006 19:30:07 -0500, Patrick Littell <[log in to unmask]>
wrote:
>>You can make do with just IF and NOT;
[snip]
>It's amazing that we can get the entirety of sentential logic from
>just these three.
[snip]

Actually we can "get them all" with just _one_; and there are two choices
for the one; we can "get them all" with NAND, and we can "get them all"
with NOR.

NOT p = p NAND p = p NOR p

p AND q = NOT (p NAND q) = (NOT p) NOR (NOT q)

p OR q = (NOT p) NAND (NOT q) = NOT (p NOR q)

IF p THEN q = p NAND (NOT q) = NOT ((NOT p) NOR q)

p XOR q = NOT(((NOT p) NAND (NOT q)) NAND (p NAND q))
= NOT(((NOT p) NOR q) NOR ((NOT q) NOR p))

p IFF q = (p NAND q) NAND ((NOT p) NAND (NOT q))
= NOT(((NOT p) NOR (NOT q)) NOR (p NOR q))

---

There was some discussion and disagreement earlier about how to interpret
the semantics of an "XOR-like" conjunction when it conjoins more than two
conjugands.  If it is treated as a mathematical operation, apparently it
would be true if an odd number of conjugands were true, and false if an
even number of conjugands were true; but this seemed an unnatural
interpretation.  Someone proposed it to mean that at least one of its
conjugands is true and at least one is false.

---

Question; In a conditional statement, for instance "if X then Y", aren't
both the condition (X) and the consequence (Y) subordinate or subjoined
clauses?  If not, which is the main clause?  If so, what is the main
clause -- what are they subordinate to?

-----

eldin
```