UCLA MATH 131A - quiz1 (3 pages)

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quiz1



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quiz1

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Pages:
3
School:
University of California, Los Angeles
Course:
Math 131a - Analysis
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Math 131A Real Analysis Quiz 1 Instructions You have 30 minutes to complete the quiz There are two problems worth a total of 30 points You may not use any books or notes Write your solutions in the space below the questions If you need more space use the back of the page Do not forget to write your name and UID in the space below Name Student ID number Question Points Score 1 15 2 15 Total 30 Problem 1 For each of the following sentences say whether it is true or false and give a one sentence reason explaining why a 4pts If Michael can carry a rhinoceros on planet Earth then Michael is simultaneously alive and dead Solution Michael cannot carry a rhinoceros so this sentence is true b 5pts x R x2 0 x 0 Solution It is false its negation x R x2 0 and x 0 i e x R x 0 x2 is true because 1 0 1 2 c 6pts N R n N n N n1 1 81 Solution It is false its negation 1 1 N R n N n N and 1 n 8 is true since we can take n max 2 dN e 1 Problem 2 In any of the following questions if you are struggling try to write out the sentence in symbolic quantifiers a 4pts Negate the following sentence Whenever given x R we can find a y R such that x y 2 Solution There is an x R with the property that for any y R x 6 y 2 b 5pts Suppose X is a set Negate the following sentence concerning X There is a function f N X with the property that whatever x we choose in X we can find an n N with f n x Solution Whatever function f N X we pick we can find an x X with the property that for all n N f n 6 x c 6pts Suppose f R R Negate the following sentence concerning f Whenever given 0 we can find a 0 with the property that x y implies f x f y Solution There is an 0 so that whatever 0 we try we can find x y R with x y and f x f y


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