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# Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA Discrete Mathematics (Math 150) Level III, Assignment 4 (2015) 1. State whether...

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Ministry of Higher Education CSTS Kingdom of Saudi Arabia SEU, KSA Discrete Mathematics (Math 150) Level III, Assignment 4 (2015) 1. State whether the following statements are True or False [9] (a) If a relation is reflexive, then it is an equivalence relation. (a) _________ (b) The relation ) 3 , 4 ( ), 2 , 4 ( ), 1 , 4 ( ), 2 , 3 ( ), 1 , 3 ( ), 1 , 2 ( R on the set 4 , 3 , 2 , 1 A is antisymmetric (b) _________ (c) A set with a partial order relation is called Poset. (c) __ _______ (d) A graph with no loops and multiple edges is called a simple graph. (d) __________ (e) An undirected graph has an even number of vertices of even degree.(e) _________ (f) In an undirected graph, the loop at a vertex contributes twice to the degree of that vertex. (f) _________ (g) A tree is a simple graph. (g)_________ (h) A rooted tree is a binary tree if every internal vertex has two children. (h)_________ (i) Vertices that have children are called external vertices. (i)_________ (Page 1 of 5)
2. Select one of the alternatives from the following questions as your answer. [9] (a) Let b a or b a b a R | ) , ( be a relation on the set of integers. Then R A. Reflexive B. Symmetric C. Transitive D. Equivalence (b) If every vertex of a directed graph has a loop, then the relation associated with it is A. Reflexive B. Symmetric C. Transitive D. Equivalence (c) The relation on a set represented by the matrix 1 1 0 0 1 0 0 0 1 R M is A. Reflexive B. Symmetric C. Transitive D. Equivalence (d) The number of edges in the wheel 3 W are A. 3 B. 4 C. 5 D. 6 (Page 2 of 5)
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Solutions
1. State whether the following statements are True or False
a) If a relation is reflexive, then it is an equivalence relation.
FALSE
A relation qualifies to be an equivalence relation...

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