hwk1 - CSE 2315 - Discrete Structures Homework 1:...

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Unformatted text preview: CSE 2315 - Discrete Structures Homework 1: Propositional Calculus and Predicate Logic CSE 2315 - Discrete Structures Homework 1- Fall 2010 Due Date: Sept. 16 2010, 3:30 pm Statements, Truth Values, and Tautologies 1. Which of the following are statements ? a) 3 + 7 = 10 b) All cars are blue. c) It will rain on Wednesday. d) There are more insects than mammals. e) Is the sun shining right now ? f) x- 3 < 7 g) 7- 4 = 9 h) Is John at home ? 2. Construct the truth tables for the following expressions and determine if they are tautologies or contradictions. a) A ∨ B → A b) (( A ∧ B ) → C ) ∨ C c) A ∧ ( C → B ) ∧ C → C ∧ A d) ( A ∨ ( A → B ) → ( B ∧ B ) e) A ↔ B ∨ C f) A ∧ B ↔ ( B → A ) 3. Let M , R , S , F , and C be the following statements: M Mary likes dogs R Cats run away from dogs S Cats are smaller than dogs F Dogs are fast C Dogs chase cats 2010 Manfred Huber Page 1 CSE 2315 - Discrete Structures Homework 1: Propositional Calculus and Predicate Logic Translate the following compound statements into symbolic notation. a) Cats are smaller than dogs and run away from them. b) If cats run away from dogs then dogs chase them. c) Only if dogs chase cats do cats run away from dogs. d) Dogs are fast and cats run away from dogs if and only if dogs chase cats. e) Mary likes dogs only if dogs do not chase cats. f) If cats are smaller than dogs and dogs are fast then cats run away from dogs and dogs chase them. Translate the following symbolic statements into English. g) M ∧ R → C h) R ∨ F ↔ C i) F ∧ M ∧ R → C j) F ∨ ( R → C ) → M k) F ↔ C l) S ∧ R ∧ C → M Proofs using Propositional Logic For all your propositional logic proofs you can use only the rules given in the following tables. In addition you are allowed to apply the deduction method. All other rules have to be proven first.addition you are allowed to apply the deduction method....
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This note was uploaded on 10/27/2010 for the course CSE 2315 taught by Professor Staff during the Spring '08 term at UT Arlington.

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hwk1 - CSE 2315 - Discrete Structures Homework 1:...

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