I am asked to translate both and , where is a propositional function that represents the statement, "x has sent an e-mail message to y," where the domain for both x and y consists of students in one's class.
I feel as though the two quantified statements would translate into the same English statement, aren't both statements the same?
This become more obvious if Q(x, y) means that y is the mother of x. Then ∀x ∃y Q(x, y) means that every person has (his or her own) mother. In contrast, ∃y ∀x Q(x, y) means that there exists a single mother of everyone.