let A= {a,b,c,d} and R= {(a,a),(a,c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. What is the inverse of R?

Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, 3),(2, 4),(4, 1),(2, 1),(1, 2),(3, 2)} (a) Is R symmetric? Justify your answer. (b) Is R transitive?

Let A = {a, b, c, d, and let R be the relation R = {(a, a), (b, b), (c, c), (d, d), (c, b), (a, d), (b, a), (b, d), (c, d), (c, a)}. Is R a total order on A? Yes No Justify your answer. (Select all that apply.) R is antisymmetric. R is not antisymmetric. There exists a chain in R that contains every element of A. There does not exist a chain in R that contains every element of A. R is transitive. R is not transitive. Each element of A exists in R. Each element of A does not exist in R. R is reflexive. R is not reflexive.

Let R be the relation on a set A = {a, b, c, d} defined by R = {(a, a), (a, b), (b, b), (b, c), (c, b), (d, c)}. Find R² and R³.