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MAS111_09_assignment_10

# MAS111_09_assignment_10 - MAS 111 FOUNDATION OF MATHEMATICS...

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Unformatted text preview: MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 10 TUTORIAL DATES: 26, 27, 28/10/2009 1. Here are some relations on a set A = { 1 , 2 , 3 , 4 , 5 } . Determine for each relation whether it is reflexive, whether it is transitive, whether is it antisymmetric. Draw the directed graph that represents each relation. (a) R = { (1 , 1) , (2 , 2) , (2 , 3) , (3 , 2) , (3 , 3) , (3 , 4) , (4 , 3) , (4 , 4) , (5 , 5) } . (b) S = { (1 , 1) , (1 , 2) , (1 , 4) , (1 , 5) , (2 , 2) , (2 , 4) , (2 , 5) , (3 , 3) , (3 , 4) , (3 , 5) , (4 , 4) , (4 , 5) , (5 , 5) } . (c) T = { (1 , 3) , (1 , 5) , (2 , 4) , (3 , 1) , (3 , 5) , (4 , 2) , (5 , 1) , (5 , 3) } . (d) U = { (1 , 1) , (1 , 3) , (1 , 5) , (2 , 2) , (2 , 4) , (3 , 1) , (3 , 3) , (3 , 5) , (4 , 2) , (4 , 4) , (5 , 1) , (5 , 3) , (5 , 5) } . 2. (a) Which (if any) of the relations in question 1 are partial orders on the set A ? In each such case draw the Hasse diagram of the partial order....
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• Spring '10
• DrChanSongHeng
• Order theory, Equivalence relation, Transitive relation, relation, Partially ordered set, partial order

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MAS111_09_assignment_10 - MAS 111 FOUNDATION OF MATHEMATICS...

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