## 辅导案例-D2L-Assignment 3

• July 29, 2020

Phil 279 Assignment 3 Part II Due: July 31, 2020 17:00 General Instructions: Please submit the following questions in a pdf or word document (no pages files!) electronically to the D2L dropbox for assignment 1. All errors lose at least 1 point. You may use the following symbols when formalizing sentences: • ∧: & • ∨: v • →: –> • ↔: • ¬: ∼ 1. Recall from part 1 the following truth function (@(A,B,C )) given by the characteristic truth table: A B C @(A,B,C ) T T T F T T F T T F T F T F F F F T T F F T F T F F T F F F F T Also recall the fact that a number of pairs of truth functions, e.g., ¬,→, are truth functionally complete on their own. We can see that because ¬(A → ¬B) represents A ∧ B , and ¬A → B represents A ∨ B , and we know ¬,∧,∨ is truth functionally complete because we can represent any truth function using those truth functions via the standard method. We also know that some binary truth functions are complete on their own. For example, using just the truth function ↑, A ↑ A represents ¬A and (A ↑ A) ↑ (B ↑ B) represents A ∨ B (see page 333 of the text). Show that @—a ternary truth function—is truth functionally complete on its own. (Hint: Consider the equivalences sheet.) (6 points, part marks are possible) 1 2. Consider the following passage: Frances, Mackenzie, and Pusheen have to meet Anouk from Monday to Thursday. None can meet on the same day, and Pusheen has to see Anouk after Mackenzie. And Frances has to go last. Thus, Mackenzie has to go first. (a) Organize the passage above into premise-conclusion form. Do not include implicit premises, but you may need to rework some sentences, and omit some things. (3 points, no part marks). (b) Provide a first-order dictionary/formalization key and domain for the argument. (4 points. Hint: Formalize this in a way that is similar to how the other FOL Frances passage was formalized.) (c) Formalize your argument in premise-conclusion form using the key you provided above. (3 points) Part marks are possible for this question. Note: Not taking the hint will result in a 0 for 1b. Remember what you have to do for the formalization key: dig out all the FOL content that you can Grammar matters! Construct your formulas properly Syntax matters! Make sure your formulas would be true iff the sentences they formalize are true. Failing to conform to these rules loses points. 2

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