Unformatted text preview: tements without using quantifiers: (a) xP (x) (b) x (x = 1 P (x)) (c) x (x = 1 P (x)) 4. Let S(x) be the statement "x is a student," L(x) be "x lives in Germany" G(x) be "x speaks German." Translate each of the following into English or into logic symbols as appropriate. The domain is the set of all people. (a) (b) (c) (d) (e) (f) (g) x (L(x) S(x)) x(L(x) S(x) G(x)) x(S(x) L(x) G(x)) There is a German speaking student Not all speakers of German live in Germany The only German residents who don't speak German are students Some students live in Germany, but some don't. 5. Determine whether each of the following pairs of sentences are equivalent. If so, explain why. If not, give an example of predicates and domains where they differ. (a) x(P (x) Q(x)); xP (x) xQ(x) (b) x(P (x) Q(x)); xP (x) xQ(x) (c) x(P (x) Q(x)); xP (x) xQ(x)...
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This note was uploaded on 02/06/2012 for the course MATHEMATIC 55 taught by Professor Robbayer during the Summer '09 term at Berkeley.
 Summer '09
 RobBayer
 Math, Logic

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