View Homework Help - CCN2241-Tutorial-6.doc from MATH S215 at The Open University of Hong Kong. Which of these relations on the set of all functions on Z !Z are equivalence relations? So for part A, you can partition people into distinct sets: First set is all people aged 0; Second set is all people aged 1; Third set is all people aged 2; Etc. Consider the set as,. Recall the following definitions: Let be a set and be a relation on the set . Powers of a Relation Let R be a relation on the set A. Another way to approach this is to try to partition people based on the relation. CCN2241 Discrete Structures Tutorial 6 Relations Exercise 9.1 (p. 527) 3. Suppose A is a set and R is an equivalence relation on A. we know that ad = bc, and cf = de, multiplying these two equations we get adcf = bcde => af = be => ((a, b), (e, f)) â R Hence it is transitive. Thus R is an equivalence relation. 4 points a) 1 1 1 0 1 1 1 1 1 581 # 3 For each of these relations on the set f1;2;3;4g, decide whether it is reï¬exive, whether it is sym-metric, whether it is antisymmetric, and whether it is transitive. Which of these relations on the set of all functions from Z to Z are equivalence relations? The objective is to tell for each of the following relations defined on the above set is reflexive, symmetric, anti-symmetric, transitive or not. First, reflexivity, symmetry, and transitivity of a relation requires that the properties are true for all elements of the set in question. Happy world In this world, "likes" is the full relation on the universe. For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, whether is it antisymmetric, and whether is it transitive. View A-VI.docx from MTS 211 at Institute of Business Administration. Determine the properties of an equivalence relation that the others lack. Symmetric relation: Which of these relations on the set of all people are equivalence relations? For each of these relations For each element a in A, the equivalence class of a, denoted [a] and called the class of a for short, is the set â¦ 2. Any relation that can be expressed using \have the same" are \are the same" is an equivalence relation. \a and b are the same age." a. This is an equivalence relation. c) f(f;g)jf(x) g(x) = 1 8x 2Zg Answer: Re exive: NO f(x) f(x) = 0 6= 1. The powers Rn;n = 1;2;3;:::, are deï¬ned recursively by R1 = R and Rn+1 = Rn R. 9.1 pg. Equivalence relations on a set and partial order Hot Network Questions Word for: "Repeatedly doing something you are scared of, in order to overcome that fear in time" Q1. You need to be careful, as was pointed out, with your phrasing of "can have" which implies "there exists", and your invocation of the $\leq$ relation to address problem (a). The identity relation is true for all pairs whose first and second element are identical. 14) Determine whether the relations represented by the following zero-one matrices are equivalence relations. Hence ( f;f) is not in relation. b. All these relations are definitions of the relation "likes" on the set {Ann, Bob, Chip}. The identity relation on set E is the set {(x, x) | x â E}. Examples. Reflexive relation: A relation is called reflexive relation if for every . Determine the properties of an equivalence relation that the others lack. For part B, you can part consider all pairs of people in the population: Ccn2241 Discrete Structures Tutorial 6 relations Exercise 9.1 ( p. 527 ) 3!... In relation matrices are equivalence relations Z to Z are equivalence relations Chip } 6 relations 9.1. And R is an equivalence relation on the set of all functions from Z to are... 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