0
$\begingroup$

F={Female students currently enrolled in an engineering program at the university of XYZ and who were born after Jan. 1,2005}

I cannot decide whether the cardinality of set F is 1 or 2 or whether this is an empty set.

The cardinality will be 1 if we say the element in set F is the whole sentence from the word Female till 2005

The cardinality will be 2 if we say the first element in set F is the sentence from the word Female till Jan. 1 and the second element is 2005; this is because of the comma.

The cardinality will be 0 if we say that this set is an empty set. This is because any student male or female who is born on (or after) 2005 will be at most 12 years old. No student of this age can be in engineering of University of XYZ.

What do you think is the cardinality of F?

Note: XYZ represents my university; its not fictional.

  • 1
    Well if it's one of the first two options then this would be a really silly trick question. – 2017-01-16
  • 2
    Very clever. But this is a question of language and semantics rather than math. I agree with Bram28 you should present all, and your professor should be happy you are thinking, but I must say if your professor was trying to trick you with either the elements being textual sentences or textual list, then he is a jerk. It is conventional that {description of things} is the set of all things satisfying the description. We can nitpick the lack of rigor of and technical shortcomings and how it won't stand up in a formal language construction... but let's do that later. – 2017-01-16
  • 0
    Do note that *everyone* were born after *some* Jan 1. – 2017-01-16
  • 0
    That is not a question about mathmatics. Should we vote what answer pleases us more? – 2017-01-16
  • 0
    @AsafKaragila I think it would be better if he notes that everone was born after some Jan1. – 2017-01-16
  • 0
    "if p is a prime number then p|((p-1)!+1)" This sentence is true because p is not a prime but a letter. – 2017-01-16

2 Answers 2

1

If this is a question your professor gave you, I would give all these possible answers with their explanation. It shows you are thinking well about this problem, which is what most professors appreciate more than any kind of one correct answer.

0

The three interpretations you give are all valid because this isn't a formally written set definition. However I would suggest that the intent is to read the sentence given as a predicate that all elements in $F$ must fulfil.

Typically if the intent was that the sentence (or sentences) was to be the elements of the set they would have quotation marks around them to disambiguate that sentences where not to be read and indicate the boundaries of the sentences.