Solution 2:

   Va    Vb   Vc   Na  Nb   Nc   Pb   Pc   Pull-up   Pull-down   Vout

    L      L     L   Off Off   Off  On   On    Yes         No            High

    L      L     H   Off Off   On  On   Off    Yes         No            High

    L      H     L   Off On    Off Off   On    Yes         No            High

    L      H     H  Off On     On Off   Off    No         Yes            Low

    H      L     L  On Off     Off On   On     Yes        Yes            X

    H      L     H  On Off     On On    Off    Yes        Yes           X

    H      H     L  On On      Off Off  On     Yes        Yes           X

    H      H     H  On On      On Off  Off      No        Yes          Low