Some providers will give unlimited traffic for things like Facebook, Twitter, LinkedIn and even YouTube in some rare cases on smartphones. I'm wondering if there's any documented way they identify this traffic. Not for malicious purposes but from an ethical standpoint I'm curious as to how they keep the data at bay. On first glance, I would assume an IP filter and payload size checks but I wonder if anyone has any better theories or resources? 


Question: Is this formula in predicate logic a tautology?
Answer: It is not a counterexample. In the case where $p$ is always true and $q$ is always false you have
$$(\forall X ,p(X) \Rightarrow q(X)) \qquad \mbox{ false}$$
$$(\forall X ,p(X) \Rightarrow q(X)) \wedge p(Y)\qquad \mbox{ false}$$
$$(\forall X ,p(X) \Rightarrow q(X)) \wedge p(Y) \Rightarrow q(Y)\qquad \mbox{ true}$$
since $\mbox{ false} \Rightarrow \mbox{ true}$ is true.