Let $C(a,b)$ be "$a$ and $b$ have communicated over the web," and the domain of discourse is all students in the class. What is the translation of "Everyone has communicated over the web with the same student" Note: the student hasn't communicated with themselves.
Very stumped on this one. I am initially stating $\forall a \exists b ((a \neq b) \implies C(a,b)).$ Is this the correct way to show that someone is not themselves in this statement?
You're very close, but currently your statement says "for all people in the class, there exists someone they've communicated with" but these $b$s needn't be the same. You're looking to say that "there exists someone in the class such that everyone else (bar themselves) has communicated with them". In practice this is the difference between:
$$ \forall a \exists b ((a \neq b) \implies C(a,b)). $$
and
$$ \exists b \forall a ((a \neq b) \implies C(a,b)). $$
The latter of which being the correct answer as @amWhy explains better, in the comments here.