On the set {a,b,c} consider the following relations:?

Question

R1={(a,a) , (b,b) , (a,c)}

R2={(a,a) , (b,b) , (c,c)}

R3={(a,a) , (a,b) , (b,a)}

for each of these relations, decide if it is reflexive, symmetric, transitive, antisymmetric. Justify your answer.

Answer 1

R1 not refexive, not symmetric; but it is transitive and antisymmetric

R2 satisfies all

R3 is not reflexive; not transitive but symmetric and antisymmetric