Let M(x, y) : "x has sent y an e-mail message"
where the domain consists of all students in your class.
Question: There is a student in your class who has sent everyone else in your class an e-mail message
My answer : $\exists x \forall y[x \not =y\land M(x, y)]$
Book answer: $\exists x \forall y[x \not =y\implies M(x, y)]$
Why is my answer wrong and why is the book answer correct?