Assignment1Solution

# Assignment1Solution - Assignment#1 Solutions and Grading...

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Assignment #1 Solutions and Grading Total Points (361 pts) Points are calculated. Your final grade is given out of 100 rounded up to the next percentage. Sample answers are given in red. Student’s answers may differ. Note: Don’t go below zero on any point calculation. Problem 1 (25 pts) Each sub-problem is worth 5 pts. All or nothing. Give partial credit in odd cases by discretion. a) 𝑞𝑞 → 𝑝𝑝 b) ( 𝑠𝑠 ∧ 𝑟𝑟 ) → 𝑞𝑞 c) 𝑝𝑝 ∧ 𝑟𝑟 ) → 𝑞𝑞 d) If I don’t finish writing my computer program before lunch and the sun isn’t shining, then I won’t play tennis in the afternoon. e) I’ll play tennis in the afternoon if, and only if, the sun is shining. Problem 2 (20 pts) 1. Points are given for the following checks (15 pts) 3 pts for each row correct (12 pts total) 3 pts for enumerating all possible p and q pairs. (-1 for each redundant pair) Note: Students may use 1 and 0 in place of true and false. The row order doesn’t matter. 𝑝𝑝 𝑞𝑞 𝑝𝑝 ∧ 𝑞𝑞 𝑝𝑝 → ( 𝑝𝑝 ∧ 𝑞𝑞 ) 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 2. 5 pts for the answer. All or nothing. 𝑝𝑝 → 𝑞𝑞

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Problem 3 (66 pts) For each problem in this section, 20 points are possible for the truth table. -1 for each row incorrect if using truth table -1 for each step incorrect using laws of logic -1 for each partial solution column missing if using truth table Heavy discretion needed. 0 points if no solution. 2 pts for the correct classification. (All neither!) a) ( 𝑝𝑝 ∧ 𝑞𝑞 ) → 𝑟𝑟� → � ( 𝑝𝑝 → 𝑟𝑟 ) ( 𝑞𝑞 → 𝑟𝑟 ) 𝑠𝑠 1 𝑠𝑠 2 𝑝𝑝 𝑞𝑞 𝑟𝑟 𝑝𝑝 ∧ 𝑞𝑞 ( 𝑝𝑝 ∧ 𝑞𝑞 ) → 𝑟𝑟 𝑝𝑝 → 𝑞𝑞 𝑞𝑞 → 𝑟𝑟 ( 𝑝𝑝 → 𝑟𝑟 ) ( 𝑞𝑞 → 𝑟𝑟 ) 𝑠𝑠 1 → 𝑠𝑠 2 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝐹𝐹 𝑇𝑇 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝐹𝐹 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 b) ( 𝑝𝑝 ∧ 𝑞𝑞 ) 𝑝𝑝 ∧ ¬ 𝑞𝑞 )
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• Fall '00
• Guha
• pts, Modus ponens, Modus tollens, Argument form, Modus tollendo ponens

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