Answer to Question #273365 in Discrete Mathematics for Joe

Question

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0,1),(1, 1), (1, 2), (2, 0), (2, 2) and (3, 0). Find the

(i) reflexive closure of R, (ii) symmetric closure of R

Answer 1

i)

The reflexive closure of a relation R on A is obtained by adding (a, a) to R for each a ∈ A

reflexive closure of R: $\{(0,1),(1, 1), (1, 2), (2, 0), (2, 2),(0,0),(3,3)\}$

ii)

symmetric closure of R is obtained by adding (b, a) to R for each (a, b) ∈ R

symmetric closure of R: $\{(0,1),(1, 1), (1, 2), (2, 0), (2, 2),(1,0),(2,1),(0,2)\}$