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HW3-W07-full

# HW3-W07-full - Homework Three CS 191 Discrete Structures I...

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Homework Three CS 191 : Discrete Structures I Feb. 20 , Winter 2007 Due Date: Mar. 6, Tuesday, before the class meeting. Section 3.1, p123 In Exercises 9-12, draw the diagraph of the relation. Exercise (11) The relation R = {(1,2), (2,3), (3,4), (4,1) } on X = {1, 2, 3, 4}. ______________________________________________________ In Exercises 13-16, write the relation as a set of ordered pairs. Exercise (14) 1 2 3 4 5 ____________________________________________________ Exercises 19-24 refer to the relation R on the set {1, 2, 3, 4, 5} defined by the rule ( x , y ) R if 3 divides x y . Exercise (20) List the elements of R -1 . __________________________________________________ 1

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Exercise (27) Is the relation of Exercise 25 reflexive, symmetric, antisymmetric, transitive, and/or a partial order? Note, the relation R of Exercise 25 is defined on the set {1, 2, 3, 4, 5} by the rule ( x , y ) R if x + y 6.. _______________________________________________________ In Exercises 29-34, determine whether each relation defined on the set of positive integers is reflexive, symmetric, antisymmetric, transitive, and/or a partial order. Exercise (30) ( x , y ) R if x > y . __________________________________________________________ Exercise (34) ( x , y ) R if 3 divides x + 2 y . ____________________________________________________________ Let R and S be relations on X. Determine whether each statement in Exercises 44-59 is true or
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HW3-W07-full - Homework Three CS 191 Discrete Structures I...

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