I'll explain why Prince's answer is unique, assuming that each question has a different correct answer. Even though this assumption wasn't stated in the question (which is a bit confusingly worded in my opinion), it seems reasonable and leads to a unique answer so I think it was intended by the original puzzle creator. (And as OP stated in the comments, we don't need to assume that each question was answered correctly by at least one person.)
First, suppose that the answer to (d) is not 1789, meaning that Anne, John and Philip all got it wrong. Since Anne, John and Philip all gave different answers for each of (a), (b), and (c), they must each have gotten exactly one question right. The only ways to assign answers to these three are:
(a) 1760, (b) 1939, (c) 1914;
(a) 1939, (b) 1914, (c) 1760; or
(a) 1914, (b) 1760, (c) 1939.
In all these cases 1760 is the answer to (a), (b), or (c), meaning that Daisy got (d) wrong. But then in all three cases Daisy has either 0 or 2 correct answers.
So the answer to (d) must be 1789. For Daisy to get a correct answer, either (b) is 1939 or (c) is 1914. In each case respectively Philip or John has 2 correct answers, so everyone must have 2 correct answers. Therefore we need both (b) 1939 and (c) 1914, and to finish it off (a) is 1760 in agreement with Prince's answer.