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quiz10 - Name Math 55 Quiz 10 August 7 2009 G51 Rob Bayer...

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Unformatted text preview: Name: Math 55 Quiz 10 August 7, 2009 G51: Rob Bayer You have until 4:00 to complete this quiz. You must show your ”Work. _ 1. (2 pts) Draw a diagram for the transitive closure of the relation with the following directed graph. You In imply add to this picture if you wish: 2. (4 pts) Let A be the set of all bit strings of length 4 and let ~ be'the relation on A given by x N y <:> a: and 3; have the same fiumber of 1‘s. . (a) Show that N is an equivalence rel tion I , I .- \ . h'_1\‘ ‘: 79",? 4V; few F; a; e17” / 7“ if: m; M tree/Ma Wis-#2. ‘... .,..'. (b) Find all elements of [1010']: {1100, low, 109!) 0W, 9191,0011; \ Ix! I a (over) 3. Consider the divisbihty' pqset given by ({1, 2, 3, 6, 12, 24, 36,48}, 1). " (a) (2 pts) Draw a Hesse diagram for this poset . , Ll <3 (b) (2 pts) What are the maximal elements, the minimal elements, the least elements, and the greatest elements? Note that some of these may not exist. W; M, 36 WW I View? I 7/€a+€;+: ,AMIQ/ ...
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