# hw2 - EECS 203 Homework 2 Solutions Section 1.3 1(E 10cde c...

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EECS 203: Homework 2 Solutions Section 1.3 1. (E) 10cde c) 5 x (C(x) Λ F(x) Λ ¬ D(x)) d) ¬ 5 x (C(x) Λ F(x) Λ D(x)) e) ( 5 x C(x)) Λ ( 5 y F(y)) Λ ( 5 z D(z)) 2. (M) 40abd a) Let F(x) = “there is less than x megabytes free on the hard disk”, W(x) = “user x is sent a warning message”. F(30) 2200 xW(x) b) Let O(x) = “directory x can be opened”, C(x) = “file x can be closed”, E = “system errors have been detected”. E (( 2200 x ¬ O(x)) Λ ( 2200 x ¬ C(x))) d) Let D(x) = “product x can be delivered”, M(x) = “there are at least x megabytes of memory available”, S(x) = “the connection speed is at least x kilobits per second”. (M(8) Λ S(56)) D(video on demand) 3. (C) 44 We can show that for some examples of P and Q, we can make the second statement true, but the first statement will be false. To do this, we choose something that is not always true so that the universal quantification of each of P and Q evaluates to false, and we get that F F which is true. Now to make the first statement false, we make sure that P and Q are not equivalent for some x, and thus we get for some x that P Q evaluates to false, and thus the universal quantification of P Q becomes false. One such example is P(x) = “x is an even number” and Q(x) = “x is a multiple of 3”, with the domain of both being the set of integers.

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