I would need some help here. I'm preparing for finals from mathematical logic and as I am browsing through some exercises, I often found these types:
Let's say we have 2 propositions $\phi$ and $\psi$:
a, construct a theory $T$ which is unsatisfiable if $\phi \vDash \psi$
b, using Skolemisation find the theory $T$ which is unsatisfiable if $\phi \vDash \psi$
I would like to get some thoughts about how to approach problems like these. Also, an example with solution would be greatly appreciated.