MAT-3110 Quiz: MATH 3110 App State Fall2013 big Quiz1 answer key
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Name: answer key: (20 points) de nition and basics. Be sure to show your work! (a) suppose that g is a non-empty set equipped an operation. 1: closure: for every a, b g, we have ab g. 2: associativity: for every a, b, c g, we have (ab)c = a(bc). 3: identity: there exists some element e g such that for all x g we have ex = xe = x. 4: inverses: for each g g there exists some g 1 g such that gg 1 = g 1g = e. 5: commutativity: ab = ba for all a, b g. (b) let g = q 0 be the non-positive rational numbers. Prove g is not a group under addition. Q 0 under addition satis es the closure axiom (non-positive plus non-positive is still non-positive), associativity holds (addition is associative), and has an additive identity (0 is non-positive).
