321s08ex1s

321s08ex1s - MAT 321 Exam I Sample Professor Sormani 1. (20...

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MAT 321 Exam I Sample Professor Sormani 1. (20 points) Let A = [ - 2 , 1] × [ - 5 , - 3]. Let B = B (3 , 4) (5). Let C = { ( x,y ) : x 2 + y 2 100 } and let D = { ( x,y ) : y = x - 5 } . a) Draw all of these sets on one chart shading them lightly if they have area. Use dashed lines if they don’t include their edges. Use solid lines otherwise. b) Which of these sets is open? c) Which of these sets is closed? d) Which of these sets is bounded? e) Which of these sets is compact? 1
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2. (20 pts) SUBSETS Let A = (1 , 3) × ( - 4 , 2). Show A B (0 , 0) (5) as follows: a) Draw a picture of the two sets carefully: b) Let ( x,y ) A then < x < and < y < c) So carefully fill in: x 2 < and y 2 < d) So x 2 + y 2 < e) Complete the proof: 2
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3. (20 pts) Proof Formating Write the first few lines of proofs of the following statements: a) p A r p > 0 such that B p ( r p ) A . 1) Let . ... 2) Choose .
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321s08ex1s - MAT 321 Exam I Sample Professor Sormani 1. (20...

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