hw1sol - Math 55: Discrete Mathematics UC Berkeley, Spring...

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Unformatted text preview: Math 55: Discrete Mathematics UC Berkeley, Spring 2009 Solutions to Homework # 1 (due January 26) § 1.1, #10: a) p ∧ ¬ q b) p ∧ q ∧ r c) r → p d) p ∧ ¬ q ∧ r e) ( p ∧ q ) → r f) r ↔ ( p ∨ q ). § 1.1, #14: a) true b) true c) false d) true. § 1.1, #23: a) converse: If I ski tomorrow, then it snows today. contrapositive: If I don’t ski tomorrow, then it doesn’t snow today. inverse: If it doesn’t snow today, then I will not ski tomorrow. b) converse: If I come to class then there will be a quiz. contrapositive: If I don’t come to class then there will be no quiz. inverse: If there is no quiz, I won’t come to class. c) converse: If a positive integer has no divisor other than 1 and itself, then it is prime. contrapositive: If a positive integer has a divisor other than 1 and itself, then it is not prime. inverse: If a positive integer is not prime, then it has a divisor other than 1 and itself. § 1.1, #27: a) p ¬ p p ∧ ¬ p T F F F T F b) p ¬ p p ∨ ¬ p T F T F T T c) p q p ∨ ¬ q ( p ∨ ¬ q ) → q T T T T T F T F F T F T F F T F 1 d) p q p ∨ q p ∧ q ( p ∨ q ) → ( p ∧ q ) T T T T T T F T F F F T T F F F F F F T e) p q p → q ¬ q → ¬ p ( p → q ) ↔ ( ¬ q → ¬ p ) T T T T T T F F F T F T T T T F F T T T f) p q p → q q → p ( p → q ) → ( q → p ) T T T T T...
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This note was uploaded on 10/10/2009 for the course MATH 55 taught by Professor Strain during the Spring '08 term at University of California, Berkeley.

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hw1sol - Math 55: Discrete Mathematics UC Berkeley, Spring...

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