Quiz3_sol - , c , b d ). ( a, b ) ( a , b ) ab = a b, (1) (...

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QUIZ 3 SOLUTIONS WED., OCT. 13 NAME: DIRECTIONS: No papers, phones, calculators, or gadgets are permitted to be out during the quiz. Show all work, clearly and in order You will lose points if any of these instructions are not followed. Questions Points Score 1 1 2 2 3 2 Total 5 1
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QUIZ 3 SOLUTIONS WED., OCT. 13 NAME: Problem 1: (1 point) What is the defnition oF an onto or surjective Function? Let f : A B be a Function. Then iF For all b B there exists an a A such that f ( a ) = b , we call f onto or surjective. Problem 2: (2 points) Let { ( a, b ) } , { ( c, d ) } be equivalence classes in Q . Recall the defnition oF the equiv- alence relation ( p, q ) ( p , q ) ⇐⇒ pq = qp . Defne multiplication in Q as { ( a, b ) } · { ( c, d ) } = { ( ac, bd ) } . Prove that multiplication is a well defned operation. Proof: We must show that For ( a, b ) ( a , b ) and ( c, d ) ( c , d ) then ( ac, bd ) ( a
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Unformatted text preview: , c , b d ). ( a, b ) ( a , b ) ab = a b, (1) ( c, d ) ( c , d ) cd = c d. (2) Multiplying the frst by cd and substituting in the second gives ab cd = a bcd = a bc d. Q. E. D. Problem 3: (2 points) Label the Following true or False (a) (0.5 points) T Q is an ordered feld. (b) (0.5 points) A feld need not be an integral domain. (c) (0.5 points) Let X be a nonempty set and ( X ) be the power set oF X . Then ( X ) with as + and as is a feld. (d) (0.5 points) A subset oF A B such that each element oF A occurs exactly once as a frst coordinate is called an injective Function. 2...
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This note was uploaded on 10/18/2011 for the course MATH 19900 taught by Professor Schmidt during the Fall '07 term at UChicago.

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Quiz3_sol - , c , b d ). ( a, b ) ( a , b ) ab = a b, (1) (...

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