e410k

# E410k - for the Quiz is A’s 80 to 100 B’s 70 to 79 C’s 60 to 69 D’s 50 to 59 1 This is the ﬁrst part of Example 11 page 254 2 S = 2 4 5 6

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MAD 2104 May 27, 2010 Quiz 4 and Key Prof. S. Hudson 1) [20pts] Compute A [2] (it’s a Boolean product), given that A = 0 0 1 1 0 0 1 1 0 2) [20pts] Deﬁne a set S Z recursively by 1) 2 S and 5 S , and 2) if a,b S then a + b S . Describe S explicitly (a list, like S = { 3 , 7 , 11 , 15 ... } is OK, or you might be able to describe S in words, or using a non-recursive formula). 3) [20pts] Suppose that 100 animals at MetroZoo are from Africa, and 50 animals are reptiles, and that 15 are reptiles from Africa. How many of the animals are either reptiles, or from Africa ? 4) [40 pts] Choose ONE: you can answer on the back. a) If a simple polygon with at least 4 sides is triangulated, then at least two of the triangles have two sides on the border [exterior] of the polygon. b) Prove that 3 n < n ! if n > 6 is an integer. Notice that 6! = 80(3 2 ) and 3 6 = 81(3 2 ), so it is not true for 6. Remarks and Answers: The average among the top 20 was approx 70 / 100. The scale
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Unformatted text preview: for the Quiz is: A’s: 80 to 100 B’s: 70 to 79 C’s: 60 to 69 D’s: 50 to 59 1) This is the ﬁrst part of Example 11, page 254. 2) S = { 2 , 4 , 5 , 6 , 7 , 8 ... } . This is exercise 7 from Ch 4.1, but rephrased in the language of Ch 4.3. Several people assumed (incorrectly) that a 6 = b , and missed that 2 + 2 = 4 ∈ S , for example. Also, see Example 7 in Ch 4.3, which is very similar. 3) 100 + 50-15 = 135 by inclusion-exclusion. Or, you can draw a Venn diagram and get 85 + 15 + 35 = 135. 4a) This is 4.2.17. See me if you want help with it. 4b) This is 4.1.20. It is the same as Example 6, which we did in class. In the Basis Step, you should compute 7! and 3 7 to see which is larger (Indirectly, I gave you some help with these numbers in last part of the problem). 1...
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## This note was uploaded on 12/27/2011 for the course MAD 2104 taught by Professor Staff during the Fall '08 term at FIU.

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