What will be the input of A and B for the Boolean expression $\overline{(A + B)}.\overline{(A.B)} =1$?

0, 0

The given Boolean expresion can be written as

$Y = \overline{(A + B)}.\overline{(AB)}$

$= (\bar A.\bar B).(\bar A+\bar B) = (\bar A.\bar A).\bar B+\bar A(\bar B.\bar B)$

$=\bar A.\bar B+\bar A.\bar B=\bar A.\bar B$

So, the truth table is