# How to declare a sentence that can only be proven true

For our maths assignment it is heavily Logic based, with some of the questions being quite confusing, such as the one below.

My lecturer has asked the following:

In Harry Potter and the Half-Blood Prince, Prof. Horace Slughorn possesses the memory of a conversation with Voldemort regarding horcruxes that Harry and Dumbledore must obtain. As it turns out, along with his many other hobbies, Horace Slughorn is an amateur logician. To jazz things up, Horace Slughorn proposes the following game to Harry Potter: By playing, Harry can win the horcrux memory, a fine aged bottle of butterbeer or a chocolate frog. Slughorn tells Harry that he must make a statement. If Harry’s statement is true, Slughorn will give him either the horcrux memory or the bottle of butterbeer. If his statement is false, Harry will get the chocolate frog. To be certain of obtaining the horcrux memory, what sentence should Harry tell Slughorn? Justify your answer.

I'm not quite sure how to formulate an answer? It could be a self reflecting answer and be 'You will not give me the butterbeer or the chocolate frog' but then Horace could just give Harry the chocolate frog proving his statement false. It could be 'you will not give me the butterbeer and give me the chocolate frog' to which could only be proven true if Horace gives Harry the chocolate frog, but does that then void his chances of getting the horcrux?

This horrible wishy washy maths is killing me. I'm no good when there's no numbers in play, could anybody help me out?

• I mildly object to the phrase "horrible wishy washy" . . . :P Nov 9, 2015 at 20:42
• I agree with Noah Schweber's comment, except for "mildly". Nov 9, 2015 at 20:45
• I'm with the OP. The question and its patronising jocular statement is tedious beyond belief. Nov 10, 2015 at 1:50
• I also find the question annoying. The extra verbiage is hard to get through and it obscures the details. for example, if H is given both the beer and the frog, does that cover all logical cases? If the statement is False then he should get the frog, which he does. If True, then the beer is a just reward. If neither True nor False, then the rules are silent so there is no problem. But is "beer + frog" an allowed move? It's all very murky.
– lulu
Nov 10, 2015 at 12:53