MATH 311W Quiz: Math 311w quiz06
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Instructions: clearly answer each of the questions below. Remember to check the back side if blank, you can use it for scrap work. Show your work and any formulas you employ. Box your answers when appropriate: suppose g = (s, ) is a group. Name the group property described by each of the logic sentences below. (a) f s g s h s (f (g h) = (f g) h) Answer:the operation is associativity (b) f s g s(f g s) Answer:the set is closed under the operation (c) e s g s(g e = e g = g) Answer:there is an identity element (d) g s j s(g j = j g = e) Answer:all elements have inverses: let g = (n, ), where we de ne g h = min(g, h). Determine which, if any, of the properties (a)-(d) in problem 1 does g satisfy. For those properties that are not satis ed, give a counter- example.
