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Shlomi Fish committed 50667e6

Add the not-a, not-b document.

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not-a-not-b-not-c.txt

+Expression:                 |ABC                            |
+                            |000|001|010|011|100|101|110|111|
+----------------------------+---+---+---+---+---+---+---+---|
+~A+~B+~C                    | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
+----------------------------+---+---+---+---+---+---+---+---|
+~A~B~C                      | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+----------------------------+---+---+---+---+---+---+---+---|
+A                           | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
+----------------------------+---+---+---+---+---+---+---+---|
+B                           | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
+----------------------------+---+---+---+---+---+---+---+---|
+C                           | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
+----------------------------+---+---+---+---+---+---+---+---|
+
+~A~B + A = A + ~B
+
+A~B = A~B
+
+~A~B~C + A = A + ~B~C
+
+A(~A+~B+~C) = A~B + A~C = A (~B + ~C)
+
+B A (~B + ~C) = AB~C (and also ~ABC and A~BC )
+
+AB~C + ~ABC = C (AB~ + ~AB) = C (A XOR B)
+
+C (AB~ + ~AB) + ABC = C (AB~ + ~AB + AB) = C (A + B)
+
+C (AB~ + ~AB) + ~A~B~C = 
+
+AB~C (A + ~B~C) = AB~C
+
+AB~C (C + ~A~B) = False
+
+A + ~B~C + B = A + B + ~C
+
+(A + B + ~C) (~A + ~B + ~C) = A~B + B~A + ~C = ~C + (A XOR B)
+
+A~B + B~A + ~C + A~C + C~A + ~B = ~B + ~C + ~A (B + C)
+
+A ( ~B + ~C + ~A (B + C) ) = A~B + A~C = A (~B + ~C)
+
+-------------------------
+
+Contemplating:
+--------------
+
+AB~C + ~A~B~C + ~AB~C + A~B~C = ~C
+
+Alternatives:
+-------------
+
+~(AB + BC + AC) = (~A + ~B)(~A + ~C)(~B + ~C) = (~A +~B~C)(~B + ~C) = 
+
+~[(A+B)(B+C)(A+C)] = ~(A+B) + ~(B+C) + ~(A+C) = ~A~B + ~B~C + ~A~C
+
+A (~A~B + ~B~C + ~A~C) = A~B~C
+
+~XY = ~X + ~Y
+
+/ ~A~B -> A + ~B ; B + ~A ; ~A~B~C ; A + ~C ; C + ~A ; ~A (~B + ~C)
+|      -> ~A~B + ~A~C
+\ ~A~C -> 
+