Simplify the following expression, using Boolean laws:

$(X+Z).(X.Y+Y.Z') + X.Z + Y$ $X.Y+Y.Z' = Y.(X+Z')$ (Distributive law - factor out Y) $(X+Z).(X.Y+Y.Z') = (X+Z).Y.(X+Z') = Y.(X+Z).(X+Z')$ $(X+Z).(X+Z') = X+Z.Z' = X+0 = X$ (Distributive law, then Complement law $Z.Z'=0$, then Identity law) So $(X+Z).(X.Y+Y.Z') = Y.X = XY$ Expression becomes: $XY + XZ + Y$ $XY+Y = Y$ (Absorption law), so $XY+XZ+Y = (XY+Y)+XZ = Y+XZ$ Final simplified expression (verified with the boolean tool): $F = Y + XZ$