"haven't" as negation of possession

I was taking a quiz in which there was a series of question about access to common objects (TV, computer, washing machine, etc.) and the two answers were "have" and "haven't". Is the usage of the latter correct? It felt really unusual and I would use "don't have" instead.

There may be a transatlantic divide here, with AmEng favouring ‘don’t have’. BrEng will normally use ‘haven’t got’. ‘Haven’t’ is also found in BrEng, but usually with an indefinite object as in ‘I'm sorry, I haven't a clue’. With a definite object in ‘I haven’t the TV’ it is certainly strange. In some contexts, even with an indefinite object, it can be formal to the point of pretentiousness, as in ‘I haven’t a TV’.

"I haven't the TV" is correct but doesn't sound very natural. A better sentence using haven't is "I haven't got the TV".

However, it sounds fine in uses such as "I haven't the nerve to sack him", "I haven't the guts for that rollercoaster", "I'm sorry, I haven't a clue".