Q.Write the truth table for the expression $Y = \overline{A}\,\overline{B} + A\overline{B}$.

Evaluating $Y = \overline{A}\,\overline{B} + A\overline{B}$ for the four combinations of A and B gives the truth table; the term $\overline{B}(\overline{A} + A) = \overline{B}$, so Y is simply $\overline{B}$. …

[!TLDR]

$Y = \overline{A}\,\overline{B} + A\overline{B} = \overline{B}$; the output is 1 whenever B = 0.

To build the truth table, each product term is evaluated for all four input combinations of A and B, and Y is 1 wherever at least one term is 1.

• $\overline{A}\,\overline{B}$ is 1 only for A = 0, B = 0.
• $A\overline{B}$ is 1 only for A = 1, B = 0. …