# Commits

committed 50667e6

# 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 -> `
`+`