Equivalence relation of
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Equivalence relation of {0,1,2,3}
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- Proof on transitive relationCRISP EQUIVALENCE RELATIONWhich of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the properties of an equivalence relation or partial order that the others lack a.{(0,0),(1,1),(2,2),(3,3)} b. {(0,0),(0,2),(2,0),(2,2),(2,3),(3,2),(3,3)} c. {(0,0),(1,1),(1,2),(2,1),(2,2),(3,3)} d. {(0,0),(1,1),(1,3),(2,2),(2,3),(3,1),(3,2),(3,3)} e. {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,2),(3,3)}
- Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} b) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)} c) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0),(2, 2), (3, 3)}What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?Triangle theorem 1. Congruence of triangles is an equivalence relation. Prove triangle theorem 1.
- How many equivalence relations on the set {1, 2, 3}?Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in terms of whether it is reflexive, irreflexive, symmetric, anti-symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. This is not a formal proof but briefly explain your reasoning.Prove showing all arguments The altitudes of concurrent