This question involves two parts.
1. Translate the argument provided in this prompt into formal logic and then use the truth-tree decision procedure (relying on Proof Tools or pencil/pen and paper) to determine whether the argument is deductively valid or invalid (entailment / non-entailment).
2. If the argument is invalid (a case of non-entailment), determine an assignment of truth values (interpretation) to the propositional letters that would show the argument to be invalid (non-entailment).
Here is the argument: John and Liz are not both at the store. John is not at the store and Frank is at the store. Therefore, Liz and Frank are both at the store.