Say the domain is all students in X university K(x, y): x knows y H(x): x is a history student
For question: some student knows all history students the answer is: ∃x∀y(H(y) --> K(x, y))
I kinda get the gist of the answer, but what is wrong with this expression? ∃x∀y(H(y) ∧ K(x, y))
For the correct answer, it is read as 'There exists some x such that for every y, if y is a history student, then x knows y.'
For the flawed expression, it is read as 'There exists some x such that for every y, y is a history student and x knows y'
My problem is, is the flawed expression wrong because it claims all students in X university are history students? Or it's due to some other reason? My understanding is only when the university only has history major will the second expression be correct, am I understanding this right?
Any assistance would be appreciated! I'm so confused.
Yes, if you use an $\land$, then every student at the university $X$ ends up becoming a history student.
Remember that the quantifiers range over the whole domain, which in this case is all students at university $X$. However, this claim is not interested in the students who are not history students. So, to restrict yourself to those, you say 'If you are a history student, then this one particular student will know you'. Which is why you want to use the $\to$