MAT-2510 Midterm: MATH 2510 App State Spring2010 Test1
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I am in the middle of proving a b, a b b . First, show (using an abbreviated truth table) that this is indeed a theorem of l. then explain why i know i"ve made a mistake if i have the following lines in my proof: 12 ( b a) (a b) /10 points) construct models whose objects are z (integers) to show that is satis able but not logically valid. [note: p (x, y) is a predicate and f (x) is a function. ] X y (p (x, y) p (f (y), f (x))) /14 points) proofs in k. (a) prove theorem k13: xa(x) xa(x) (b) prove theorem k31: x(a(x) b(x)) ( xa(x) xb(x)) /14 points) how aboutmore proofs? (a) use induction to show that 1 + 4 + 7 + + (3n 2) = 1. 2 n(3n 1) for all positive integers n. (b) prove that 2 is irrational.
