I have the following statement:
"Only those who play in orchestra are blonde."
Does it tell me something about the whole group of people who play in orchestra? For example, why can't I say that all who play in orchestra are blonde?
According to the book, from which it was taken, it is said that the statement
"All people who are not blonde don't play in orchestra."
is false. So my question is - why? If it is false then there are some other groups of people with different hair color who can play orchestra. But it is a contradiction. For example, if the statement was: "Only those who have the ticket can buy TV", it is right to say that "All who can't buy TV don't have the ticket" (regardless the real life and based only on the statement/condition that is given). We are told in the first statement that only members of some group (those who play orchestra) have some characteristic (are blonde). So logically, those who don't have this specific characteristic don't belong to that group. Don't they?
Another example that I thought about: say that the base statement was:
"Only the smartest students get 100 points out of 100 in the exam."
So according to what the books says regarding the statement in the previous example, the following statement will be false:
"All those who don't get 100 points are not the smartest students."
So it seems that the main problem here is that I can't determine whether all the smartest students get 100 or not. These "only" and "all" are really confusing.
Sorry if it sounds stupid, but I'm stuck with that.