$\left(\forall x \cdot p(X) \Rightarrow q(X)\right) \wedge p(Y) \Rightarrow q(Y)$

At first glance this seems like a tautlogy and that's what my notes say. But an interpretation where $p$ is always true and $q$ is always false seems to be a counterexample.

Can someone confirm this or show me where I've gone wrong? 

Thanks.


Question: How should I store leftover rice noodles?
Answer: From the point of view of someone who used to work in a Chinese restaurant, we used to prepare vermicelli which are really thin rice noodles by soaking the uncooked dry noodles in cold water for about 1 hour or until it is flexible. We then can store this soaked, but uncooked noodle covered with a plastic wrap in the refrigerator for several days. They don't need to be oiled. To cook it, we just submerge it in boiling water for about a minute and then prepare it however we need it. With the soak it takes practically no time to cook at all.

Perhaps in the future you can follow this method and pre-soak your noodles. Then you can use however much noodles you need from that batch and save the rest for later. Plus it'll save on cooking time.