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On Thu, 16 Mar 2006 19:30:07 -0500, Patrick Littell <[log in to unmask]> 
wrote:
>On 3/16/06, 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?

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eldin