The difference between "if" and "and" in symbolic logic

Let M(x,y) be “x has sent y an e-mail message” and T(x,y) be “x has telephoned y,” where the domain consists of all students in your class. Assume that all e-mail messages that were sent are received. Use quantifiers to express each of these statements.

1. There is a student in your class who has not received an e-mail message from anyone else in the class and who has not been called by any other student in the class.

2. Every student in the class has either received an email message or received a telephone call from another student in the class.

The answer in book for 1 is:

$\exists x\forall y(x\ne y\to (\neg M(y,x)\wedge \neg T(y,x)))$

and the answer for 2 is:

$\forall x(\exists y(x\ne y\wedge (M(y,x)\vee T(y,x)))).$

My problem is with parts $x\ne y\phantom{\rule{mediummathspace}{0ex}}\wedge $

and $x\ne y\to .$.

When should I use "→" or "∧" after $x\ne y?$ I don't understand the difference in their literature in the question. When I want to use "if" in any other question, the answer is "and" and vice versa.