Hi Wayne,
Haven't read your last questionn, but if it has a 240v AC adaptor to 12V then you can plug it straight into a 3 pin 240v plug socket if there is one close to your TV point. This of course assumes that you have a 240v hook up to the caravan!
If you only have a 12v power point then you will need a suitable power plug to connect directly to the TV power-in socket. Based on your description of the AC adaptor, the TV must run on 12 Volts.
Sproket is right to raise a word of caution here and the link he has provided does provide valid information.
Having said that, I have run our 15" LCD Matsui TV with built in DVD for 3 years now off the 12v feed in our Swift caravan with no problems so far. Perhaps I have been lucky. The reason for this is that the TV is permanently fitted to a swivel mount and I didn't want the extra bulk of the AC adaptor strapped to the mount.
The other reason I run it on 12 volts is because whilst on a hook up, I like to switch off the battery charger once in a while to let the caravan battery earn its keep and discharge a little. Never to the point of allowing it to go flat, and strangely the TV sound stops working when the battery voltage drops too far which is the que for switching back on the charger!! I have no scientific proof that this is a good or bad thing for the battery, but we are still on the same battery I bought 7 years ago.