1 a given a 1 2 3 4 5 6 7 8 9 consider the following relation on a r 1

Question

1)
a. Given A = {1, 2, 3, 4, 5, 6, 7, 8, 9). Consider the following relation on A.
R = {(1,1), (1,4), (1,9), (2,2), (3,3), (4,1), (4,4), (9,1), (9,1), (9,9)}
Determine whether R is reflexive, symmetric, transitive or antisymmetric,
Give reasons for each of these four (4) types.
b. Given R₁ and R₂ be the relations on set A = {1, 2, 3, 4).
R₁ = {(1,2), (1,3), (2,4), (4,4)}
R₂ = {(1,1), (1,2), (1,3), (2,3), (2,4)}
(i) Represent the relations R₁ and R₂ as a zero-one matrix.
(ii) Represent the relations R₁ and R₂ as a directed graph.
(iii) Fine the matrices that represent R₁ 0 R₂ and R₁0 R₁.