4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective relation C: reflective and not symmetric relation A O B Ос
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- 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)}Let A = {1, 2, 3, 4, 6}. Let Ri be a relation defined on A. a. Verify reflexive property on the relation R1= {(1, 1), (1, 2), (2, 2), (3, 3), (3, 4), (4, 4), (6, 6)}.b. Verify symmetric property on the relation R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 3), (4, 4)}.c. Verify asymmetric property on the relation R3 = {(1, 2), (2, 4), (3, 4), (4, 6), (6, 6)}.d. Verify antisymmetric property on the relation R4 = {(1, 1), (1, 2), (2, 3), (3, 3), (3, 4), (6, 3)}e. Verify transitive property on the relation R5 = {(1, 2), (1, 3), (1, 6), (2, 3), (3, 4), (4, 6), (3, 6)}.True or False? Let R be an equivalence relation on A = {w, x, y, z}. If wRx, yRz, and wRz, then xRy.
- Which 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)}Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c), (c, d), (d, d)} be arelation on A. Which of the properties reflexive, symmetric and transitive does the relation R possess? If Rdoes not possess one of these properties, explain why. How do I know where to stop? How do I know when I have proven transitivity? for example? I have difficulties with knowing if my prove is complete or notWhat is equivalence relation
- Which of these relations on {0, 1, 2, 3} are equivalence relations? *CRISP EQUIVALENCE RELATIONLet 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.
- Basic Topological SpacesLet ℝ denote the set of real numbers, and β:={(x,y)∈ℝxℝ| xy≥∅} be a relation on ℝ. Which properties does β satisfy? Explain.Give examples: For each of the four relations between natural numbers x and y in the left column of the table below, and each of the three properties of relations in the top row, indicate whether the given relation has the given property. Write yes or no in each cell. {(x,y) | x <- N, y <- N, relation}reflexivesymmetrictransitivex /= y x >= y x + y >= 10 even (x + y)