Yes, you can do it. Depending on the quirks of OS/X you may need to different OS installations on the SSD. That would be slightly more space using, but not a real problem.

However USB2 is slow. Sequential transfer rates via the USB2 bus are about 35MB/second, way slows than a HDD or a SSD.  You would gain some performance gain on random IOs, but I expect the nett result to be a lot slower.

Now if you can replace the external USB casing with something faster (e.g. eSATA or thunderbolt) then: Yes, it will work and be a lot faster.

SSD Drive - external vs Internal
$\left(\forall x \cdot p(X) \Rightarrow q(X)\right) \wedge p(Y) \Rightarrow q(Y)$

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.
