HW1-Solutions - EECS 203: DISCRETE MATHEMATICS Homework 1...

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EECS 203: DISCRETE MATHEMATICS Homework 1 Solutions 1.1.10 a. r ∧¬ q b. p q r c. r p d. p ∧¬ q r e. ( p q ) r f. r ( q p ) (this English sentence could also be translated as r ( q p ).) 1.1.14 a. True. Since “1 + 1 = 3” is false, the implication “1 + 1 = 3” “unicorns exist” is true regardless of whether unicorns exist. b. True. Same reason as a . c. False. The implication “1 + 1 = 2” “dogs can fly” is true except when “1+1=2” is true (which it is) and “dogs can fly” is false (which it is.) d. True. Both 2 + 2 = 4 and 1 + 2 = 3 are true. 1.1.26 (a) 4. There are two atomic propositions ( p and q ) and two possibilities for each (T and F). (b) 8. Three atomic propositions, 2 3 = 8. (c) 64 = 2 6 . (d) 32 = 2 5 . 1.1.28 p q p → ¬ p p ↔ ¬ p p ( p q ) ( p q ) ( p q ) ( q → ¬ p ) ( p q ) ( p q ) ( p ↔ ¬ q ) T T F F F T F T T F F F F T F T F T T F T T F T F F T F F T T T 1.2.12 a.
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HW1-Solutions - EECS 203: DISCRETE MATHEMATICS Homework 1...

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