In Catan, how to ensure nobody lies when monopoly card is played?
Count the cards in the supply

In Settlers of Catan you are always allowed to count the number of resources left in the supply decks.  It is a perfectly legal move to count the deck before using the monopoly on a resource.  

This also means that after you got the resources you can just check how many you have in your hand, and how many are left in the deck.  If you are missing one, then someone is cheating.

In the 4th edition of the game there are 19 of each resource card.

Even if you think that counting the deck is out of the spirit of the game, having someone do it after a monopoly reveals no new information, and just controls for cheating.