1. The problem statement, all variables and given/known data Taken from Discrete Mathematics and its Applications, Seventh Edition: "What is wrong with this argument? Let [itex]S(x, y)[/itex] be '[itex]x[/itex] is shorter than [itex]y[/itex].' Given the premise [itex]\exists s S(s, Max)[/itex], it follows that [itex]S(Max, Max)[/itex]. Then by existential generalization it follows that [itex]\exists x S(x, x)[/itex], so that someone is shorter than himself." 2. Relevant equations A similarly worded question (i.e., it begins with, "What is wrong with this argument?...") has its answer in the back of the book. The answer is as follows: "We know that some [itex]x[/itex] exists that makes [itex]H(x)[/itex] true, but we cannot conclude that [itex]Lola[/itex] is one such [itex]x[/itex]." 3. The attempt at a solution Prior to looking at the answer to the similar question in the back of the book, I thought that perhaps I was being asked to identify what logical error was being made (e.g., fallacy of affirming the conclusion, fallacy of denying the hypothesis, etc.). However, the answer to the similarly worded question is very plainspoken (for lack of a better term). So I figured they'd be looking for an answer that looks like one of the following: (1)-[itex]s[/itex] isn't apart of the given domain ([itex]x[/itex] or [itex]y[/itex]). (2)-It doesn't follow that [itex]S(Max,Max)[/itex] given [itex]∃sS(s,Max)[/itex]. (3)-A person can't be shorter than his or herself (i.e., [itex]x \not< x[/itex]). That's impossible. (4)-[itex]x[/itex] is distict from [itex]y[/itex] (i.e., [itex]x \not= y[/itex]). (5, which is what I'd say is the answer)-Some combination of answers 3 and 4. (I realize that some of these are kind of saying the same thing.) A student peer tutor has said that none of those are the correct answers. What's wrong with these answers? If the answer, "We don't know that [itex]Lola \in x[/itex]," will satisfy a similar question, what's wrong with these? As I said, my first choice for my answer would be (5).