F = !B & ( A + !(A&B) ) = !B & (A + !A + !B) = !B & (1+!B)= !B
{ т.к. !(A&B) = !A + !B }
F = !(A&B) + A&!B + A&B + B&C = !A + !B + A + B&C = !B + B&C
{ т.к. !(A&B) = !A + !B, A&!B + A&B = A&(!B+B) = A }
F = !(A&B + B&C) + C&!A = (A&B + B&C) & !(C&!A) =
= (A&B + B&C) & (!C+A) = B&(A+C)&(A+!C) = B & A
{ т.к. (A+C)&(A+!C) = AA + A!C + CA + C!C = A + A(!C+C)+0 = A + A = A }