c) f(f;g)jf(x) g(x) = 1 8x 2Zg Answer: Re exive: NO f(x) f(x) = 0 6= 1. View Homework Help - CCN2241-Tutorial-6.doc from MATH S215 at The Open University of Hong Kong. Suppose A is a set and R is an equivalence relation on A. Thus R is an equivalence relation. The objective is to tell for each of the following relations defined on the above set is reflexive, symmetric, anti-symmetric, transitive or not. Which of these relations on the set of all people are equivalence relations? Examples. For each element a in A, the equivalence class of a, denoted [a] and called the class of a for short, is the set … 4 points a) 1 1 1 0 1 1 1 1 1 The identity relation is true for all pairs whose first and second element are identical. \a and b are the same age." Q1. 2. View A-VI.docx from MTS 211 at Institute of Business Administration. Which of these relations on the set of all functions from Z to Z are equivalence relations? This is an equivalence relation. The identity relation on set E is the set {(x, x) | x ∈ E}. CCN2241 Discrete Structures Tutorial 6 Relations Exercise 9.1 (p. 527) 3. a. 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). Any relation that can be expressed using \have the same" are \are the same" is an equivalence relation. Symmetric relation: Happy world In this world, "likes" is the full relation on the universe. Determine the properties of an equivalence relation that the others lack. First, reflexivity, symmetry, and transitivity of a relation requires that the properties are true for all elements of the set in question. 581 # 3 For each of these relations on the set f1;2;3;4g, decide whether it is reflexive, whether it is sym-metric, whether it is antisymmetric, and whether it is transitive. Powers of a Relation Let R be a relation on the set A. 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. b. Another way to approach this is to try to partition people based on the relation. For each of these relations 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,. we know that ad = bc, and cf = de, multiplying these two equations we get adcf = bcde => af = be => ((a, b), (e, f)) ∈ R Hence it is transitive. For part B, you can part consider all pairs of people in the population: All these relations are definitions of the relation "likes" on the set {Ann, Bob, Chip}. Recall the following definitions: Let be a set and be a relation on the set . 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