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? ----- eldin