Simplify the following expression, using Boolean laws:

$A.(A'+B).C.(A+B)$ $A.(A'+B) = A.A' + A.B = 0 + AB = AB$ (Distributive law, then Complement law) Expression becomes: $AB.C.(A+B) = ABC.(A+B)$ $ABC.(A+B) = ABC.A + ABC.B = ABC + ABC = ABC$ (Distributive law, then Idempotent law) Final simplified expression (verified with the boolean tool): $F = ABC$