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# hw1 - From Section 1.2 problems 2 3 4 5 6 8 9 12 16 19 20...

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EE 369 Homework ============================================================================== REMINDER: Collaboration must end before writing begins (on each problem separately). See the initial course information handout. ============================================================================== Below, we use the abbreviations: ^ for "and", v for "or", --> for "implies", |= for "entails", and P' for the negation of P. In preparing your solution, please use these abbreviations. If other non-text symbols come up, ask [email protected] how to abbreviate them. Please read sections 1.1 and 1.2 in the Gersting textbook (but skip the section called "An Algorithm" on pp. 11-13) All problems apply to course outcome 1. Solve the following problems. 4 points per problem (except 8 points for E5). From Section 1.1: problems 10, 13, 17, 33, 37, 43
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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....
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