Suppose we assume the logic has just 5 statement letters (i.e. Boolean variables): A, B, C, D, and E.

E1. Show a model that is a counterexample to (A ^ B) |= (B --> (not C))?

E2. Expand the definition of entailment in the following two statements, explaining without using "entails" what they mean:

a. P |= (Q v R)

b. either (P |= Q) or (P |= R) or both Here, P, Q, and R are arbitrary formulas.

E3. Prove that 2a and 2b are not necessarily the same by finding formulas P, Q, and R for which one is true and the other is false.