Page 21 - Discrete Structure II

R = { (1,1), ( 2, 1), (1, 3) ( 2, 3), (3,2)}

(1, 1) ---- (1, 3) ----- (1,3) a = b and b= c then a = c (a, b) and (b,c) --- (a, c)

(2,1) -----(1, 1)________> (2,1)
(2,1) -----(1, 3)--------- (2, 3)

(1,3) --- (3, 2) ---- (1,2)

(2,3) ----(3, 2) ---- (2, 2)

R2 = { (1,1), ( 2, 1), (1, 3) ( 2, 3), (3, 2), (3,1) }
(1, 1) and (1, 3) -- (1, 3)

(2, 1) and (1, 1) ------(2,1)

(2, 1) and (1, 3) ----(2, 3)

(1, 3) and (3, 2) ----(1, 2)

(1, 3) and (3, 1)-----(1,1)

R3 = { (1,1), ( 2, 1), (1, 3) ( 2, 3), (3, 2), (3, 3) }

(1, 1) and (1, 3) ---------(1, 3)

(2,1) and (1, 1) ------(2,1)

(2,1) and (1, 3)-------(2, 3)

(1,3) and (3, 2 ) ----(1, 2)
It is not transitive

Exercise

4