# ws2 - Rob Bayer Instructions Math 55 Worksheet Introduce...

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Rob Bayer Math 55 Worksheet June 23, 2009 Instructions Introduce yourselves! Despite popular belief, math is in fact a team sport! Find some blackboard space, a piece of chalk, and decide who will be your ﬁrst scribe. Do the problems below, having a diﬀerent person be the scribe for each one. Try to work out the problems as a group, but feel free to ﬂag me down if you run into a wall. Predicates and Quantiﬁers 1. If P ( x ) is the statement “x > 0” and G ( x,y ) is the statement x 2 y , determine the truth value of each of the following (a) P (1) (b) G (2 , - 3) (c) P ( - 1) G ( - 2 , 1) 2. Using the same predicates as above, determine the truth values of each of the following statements if the domain is the set of all real numbers. (a) xP ( x ) (b) xP ( x ) ∧ ∀ xG ( x, 0) (c) yG (2 ,y ) 3. Suppose the domain of P ( x ) consists of the integers 0,1,2,3. Re-write each of the following statements without using quantiﬁers: (a) xP ( x ) (b) x ( x 6 = 1 P ( x )) (c) x ( x 6 = 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)

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ws2 - Rob Bayer Instructions Math 55 Worksheet Introduce...

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