simplify with Boolean algebra
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A+´AB=1.
´AB(A+ˊB)(ˊB+B)=ˊA.
( A+C)(AD+AˊD)+AC+C=A+C.
A+AB=A.
ˊA(A+B)+(B+AA)(A+ˊB)=A+B.
BC+BˊC+BA=B.
A+ˊAB+ˊAˊBC+ˊAˊBˊCD+ˊAˊBˊCˊDE=A+B+C+D+E.
A(A+B)=A
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