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Homework 1 Solutions

# Homework 1 Solutions - 1.1 Problem 8(a"If you have the flu...

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§ 1.1 Problem 8 ( a ): “If you have the flu then you miss the final exam.” ( b ): “You don’t miss the final exam if and only if you pass the course.” ( c ): “If you miss the final exam then you do not pass the course.” ( d ): “You have the flu or you miss the final exam or you pass the course.” ( e ): “It is either the case that, if you have the flu you don’t pass the course, or that, if you miss the final exam you don’t pass the course.” ( f ): “Either you both have the flu and miss the final exam, or else you both take the exam and pass the course.” § 1.1 Problem 11 ( a ): r ∧ ¬ p ( b ): ¬ p q r ( c ): r ( q ↔ ¬ p ) ( d ): ¬ q ∧ ¬ p r ( e ): ( q ( ¬ r ∧ ¬ p )) ∧ ¬ ( ( ¬ r ∧ ¬ p ) q ) ( f ): ( p r ) → ¬ q § 1.1 Problem 24 ( a ): p p → ¬ p T F F T ( b ): p p ↔ ¬ p T F F F ( c ): p q p ( p q ) T T F T F F F T T F F F ( d ): p q p q p q ( p q ) ( p q ) T T T T T T F F T T F T F T T F F F F T ( e ): p q q → ¬ p p q ( q → ¬ p ) ( p q ) T T F T F T F T F F F T T F F F F T T T 1

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( f ): p q p q p ↔ ¬ q ( p q ) ( p ↔ ¬ q ) T T T F T T F F T T F T F T T F F T F T § 1.1 Problem 45: Let M =“The system is in multiuse state,” N =“The system is operating normally,” K =“The kernel is functioning” and I =“The system is in interrupt mode.” We have the statements M N N K - K I ¬ M I ¬ I We could use a truth table with 16 lines to determine whether it is possible for all the statements to be true at the same time. However, that’s tedious. Instead, let’s try to satisfy them all and see what the truth values of M , N , K and I have to be. First of all, ¬ I tells us that I must be false. Because of this, the statement ¬ K
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