Justify whether the following relations are reflexive, symmetric, transitive, or antisymmetric. Also, determine if they are...

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Justify whether the following relations are reflexive, symmetric, transitive, or antisymmetric. Also, determine if they are equivalence relations or partial order relations. (20 pts) (1) R₁ = Ø (R₁ is a relation on {5,6,7}) (ii) R₂ = {(x,y) = PxP:x and y study at Penn State) (P is the set of all people who study at Penn State) (iii) R3 = {(0,0), (1, 1), (2,2), (0, 1), (1,0)} (R3 is a relation on Z) (iv) R4 = {(0,0), (1, 1), (2,0), (2, 2), (2,3), (3,3)} (R4 is a relation on {0, 1,2,3}) (v) R5 = {(a,b) = PxP: a b or a is a descendant of b} (P is the set of all people) Justify whether the following relations are reflexive, symmetric, transitive, or antisymmetric. Also, determine if they are equivalence relations or partial order relations. (20 pts) (1) R₁ = Ø (R₁ is a relation on {5,6,7}) (ii) R₂ = {(x,y) = PxP:x and y study at Penn State) (P is the set of all people who study at Penn State) (iii) R3 = {(0,0), (1, 1), (2,2), (0, 1), (1,0)} (R3 is a relation on Z) (iv) R4 = {(0,0), (1, 1), (2,0), (2, 2), (2,3), (3,3)} (R4 is a relation on {0, 1,2,3}) (v) R5 = {(a,b) = PxP: a b or a is a descendant of b} (P is the set of all people)

Answer rating: 100% (QA)

i R R is a relation on 567 Reflexive A relation R is reflexive if a a is in R for every element a in the set In this case R contains the pairs 5 5 6 6 and 7 7 so it is reflexiveSymmetric A relation R ... View the full answer