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Unformatted text preview: EECS 203: DISCRETE MATHEMATICS Homework 2 Solutions 1. (10 points) Chapter 1.4, Problem 10 Solution : (a) ∀ xF ( x, Fred ) (b) ∀ yF ( Evelyn, y ) (c) ∀ x ∃ yF ( x, y ) (d) ¬ ( ∃ x ∀ yF ( x, y )) ≡ ∀ x ∃ y ¬ F ( x, y ) (e) ∀ x ∃ yF ( y, x ) (f) ∀ x ( ¬ F ( x, Fred ) ∨ ¬ F ( x, Jerry )) (g) ∃ x ∃ y ( F ( Nancy, x ) ∧ F ( Nancy, y ) ∧ x 6 = y ∧ ∀ z ( F ( Nancy, z ) → ( z = x ∨ z = y ))) (h) ∃ y ( ∀ xF ( x, y ) ∧ ∀ z ( ∀ xF ( x, z ) → ( z = y ))) (i) ∀ x ( ¬ F ( x, x )) (j) As many of you pointed out, this sentence is slightly ambiguous since it is unclear whether that one person must fool himself or doesn’t necessarily fool himself. We assume the latter. ∃ x ∃ y ( F ( x, y ) ∧ x 6 = y ∧ ∀ z ( F ( x, z ) → ( z = x ∨ z = y ))) 2. (6 points) Express “Every even number greater than 2 is the sum of two primes” as a quantified formula. Your formula can make use of logical operators and quantifiers ( ∀ , ∃ , ∧...
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 Fall '07
 YaoyunShi
 Logic, Number Theory, Prime number, Predicate logic, Quantification, twin primes

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