Unformatted text preview: From Section 1.2: problems 2, 3, 4, 5, 6, 8, 9, 12, 16, 19, 20, 37, 46 Additional problems on entailment: Suppose we assume the logic has just 5 statement letters: A, B, C, D, and E. E1. How many models are there for the formula A ^ B? E2. How many models are there for the formula B --> (not C)? E3. Show a model that is a counterexample to (A ^ B) |= (B --> (not C))? E4. 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. E5. Prove that 4a and 4b are not necessarily the same by finding formulas P, Q, and R for which one is true and the other is false....
View Full Document
- Spring '08