Flood disasters are the most frequent disasters in Malaysia, especially during the monsoon seasons. The robust structure developed by Malaysia's National Security Council $($MKN$)$ is utilized to manage disasters in the country. This structure consists of four members: The Prime Minister, along with the Heads of National, State, and District Disaster Management and Relief Committees.

The evacuation system is to be activated by a device obeying the rules: the evacuation can only be initiated if the Prime Minister and at least one of the three Heads given their permissions.

Design the evacuation activation circuit using both Boolean algebra and Karnaugh map methods. Implement the circuit using minimum $2-$input basic logic gates.

Finally, implement an alternative logic circuit using minimum combination of $2-$inputs NAND gates only.