Consider the following relations on A = {0, 1, 2, 3, 4}. Determine which are reflexive...

    

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Consider the following relations on A = {0, 1, 2, 3, 4}. Determine which are reflexive which are symmetric, which are transitive, and which are equivalence relations (Circle/State all that apply and Cross out/State all that do not apply). If a relation is an equivalence relation, give the associated partition A/Ri, i.e., give A modulo Ri. If a relation is not an equivalence relation, you may either leave the blank for A/R blank or write 'NA'. (i) Ro={(0,0), (1, 1), (2, 2), (3, 3), (4, 4)} Reflexive A/Ro= Symmetric Transitive Equivalence Relation (ii) R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (3, 1)} Reflexive A/R1 = Symmetric Transitive Equivalence Relation (iii) R2 = {(0,0), (0, 2), (0, 4), (1, 1), (1, 3), (2, 2), (2, 4), (3, 3), (4, 4)} Reflexive Symmetric Transitive Equivalence Relation A/R2 = = (iv) R3 = {(a, b) E A A | ab is even} Reflexive A/R3 = Symmetric Transitive Equivalence Relation (v) R = {(a, b) A A | ab is odd} - Reflexive A/R4= = Symmetric (vi) R5 = = {(a, b) A A | 3|(a - b)} Reflexive A/R5 = = Symmetric Transitive Equivalence Relation Transitive Equivalence Relation Consider the following relations on A = {0, 1, 2, 3, 4}. Determine which are reflexive which are symmetric, which are transitive, and which are equivalence relations (Circle/State all that apply and Cross out/State all that do not apply). If a relation is an equivalence relation, give the associated partition A/Ri, i.e., give A modulo Ri. If a relation is not an equivalence relation, you may either leave the blank for A/R blank or write 'NA'. (i) Ro={(0,0), (1, 1), (2, 2), (3, 3), (4, 4)} Reflexive A/Ro= Symmetric Transitive Equivalence Relation (ii) R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (3, 1)} Reflexive A/R1 = Symmetric Transitive Equivalence Relation (iii) R2 = {(0,0), (0, 2), (0, 4), (1, 1), (1, 3), (2, 2), (2, 4), (3, 3), (4, 4)} Reflexive Symmetric Transitive Equivalence Relation A/R2 = = (iv) R3 = {(a, b) E A A | ab is even} Reflexive A/R3 = Symmetric Transitive Equivalence Relation (v) R = {(a, b) A A | ab is odd} - Reflexive A/R4= = Symmetric (vi) R5 = = {(a, b) A A | 3|(a - b)} Reflexive A/R5 = = Symmetric Transitive Equivalence Relation Transitive Equivalence Relation