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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 doesnt 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