Homework on §1.4—assigned Fri 9/3 and due Mon 9/6

For each of the following claims of entailment, describe a counterexample—that is, in each case, describe a possible world that shows the claim of entailment to be false by dividing its assumptions from its conclusion. (To describe the possible world, just say what truth values the sentences φ, ψ, and χ would have in it.)

(i)

φ, ψ ⊨ χ

(ii)

ψ, χ ⊨ φ

Could one possible world serve as counterexample to both claims? That is, could a single possible world divide the assumptions from the conclusion in both cases? (Say why or why not.)