riddle-not-a-not-b-not-c / not-a-not-b-not-c.txt

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85``` ```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 -> ```