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hwk1_sol - CSE 2315 Discrete Structures Homework 1...

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CSE 2315 - Discrete Structures Homework 1: Propositional Calculus and Predicate Logic CSE 2315 - Discrete Structures Homework 1- Solutions - Fall 2010 Due Date: Sept. 16 2010, 3:30 pm Statements, Truth Values, and Tautologies 1. a) Is a statement. b) Is a statement. c) Is a statement. (Truth value does not have to be known.) d) Is a statement. e) Is not a statement. (Questions can not be statements.) f) Is not a statement. (Is not strictly true or false because of the variable.) g) Is a statement. h) Is not a statement. (Questions can not be statements.) 2. a) A B A B A B A T T T T T F T T F T T F F F F T b) A B C A B ( A B ) C C (( A B ) C ) C T T T T T F T T T F T F T T T F T F T F T T F F F T T T F T T F T F T F T F F T T T F F T F T F T F F F F T T T is a tautology 2010 Manfred Huber Page 1

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CSE 2315 - Discrete Structures Homework 1: Propositional Calculus and Predicate Logic c) A B C C B A ( C B ) A ( C B ) C A C A A ( C B ) C C A T T T T T T F F F T T F T T F F F T T F T F F F F F T T F F T T F F F T F T T T F F T T T F T F T F F T F T F F T F F F T T T F F F T F F T F T d) A B A B A ( A B ) B B B ( A ( A B )) ( B B ) T T T T F F T T F F T T F T F T T T F F T F F T T T F T is a tautology e) A B C B C A B C T T T T T T T F T T T F T T T T F F F F F T T T F F T F T F F F T T F F F F F T f) A B A A B B A A B ( B A ) T T F F T F T F F F T F F T T T F F F F T F T F is a contradiction 3. a) S R b) R C c) C R d) F R C e) C M f) ( S F ) ( R C ) g) If Mary likes dogs and cats do not run away from dogs then dogs do not chase cats. 2010 Manfred Huber Page 2
CSE 2315 - Discrete Structures Homework 1: Propositional Calculus and Predicate Logic h) Dogs chase cats if and only if cats run away from dogs or dogs are fast. i) IF dogs are fast and Mary likes dogs and cats do not run away from dogs then dogs do not chase cats.

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hwk1_sol - CSE 2315 Discrete Structures Homework 1...

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