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riddle-not-a-not-b-not-c / 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~C+A~B~C             | 1   1   1   0   1   0   0   0 |
----------------------------+---+---+---+---+---+---+---+---|
~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)

AB~C + ~A~B~C = ~C (AB + ~A~B)

(~B + ~C + ~A (B + C) )*(B+C) = ~BC + ~CB + ~A(B + C) = ~BC + ~CB + ~AB + ~AC
= B (~A + ~C) + C (~A + ~B)


-------------------------

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

A~B~C + ~AB~C = ~C(A XOR B)

~A~B + ~B~C + ~A~C + A = A + ~B + ~C

A~B~C + ~AB~C + C = (A XOR B) + C = C + A~B + ~AB

B*(C + A~B + ~AB) = BC + ~AB = B (C + ~A)

BC + ~AB + ~BA + AC = C(A + B) + (A XOR B)

A~B~C + B  = B + A~C

(B + A~C) + (~A~B + ~B~C + ~A~C) = ~A + ~C + B

(A + ~B + ~C) * (~AB~C) = ~AB~C

/ ~A~B -> A + ~B ; B + ~A ; ~A~B~C ; A + ~C ; C + ~A ; ~A (~B + ~C)
|      -> ~A~B + ~A~C
\ ~A~C -> 
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