Suppose that R1 1 2 2 1 R2 1 2 1 3 3 1 3 2 4 1 4 2 R3 1 1 2

Suppose that R_1 = {(1, 2), (2, 1)} R_2 {(1, 2), (1, 3), (3, 1), (3, 2), (4, 1), (4, 2)} R_3 {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4, 4)} R_4 {(1, 4), (2, 1), (3, 2)} R_5 {(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)} R_6 {(1, 1), (2, 2), (3, 3), (4, 4)} Determine which of these statements are correct. Check ALL correct answers below. R_5 is transitive R_3 is transitive R_6 is symmetric R_1 is antisymmetric R_1 is transitive R_6 is antisymmetric R_6 is transitive R_1 is asymmetric R_4 is transitive R_4 is asymmetric

Solution

A . R5 is transitive . as there is a relation between 1,2 ans 3 like 2-->1 , 3--> 2 => 3-->1 .

B. R3 is not transitive as there no relation between 1,3 and 4

E. R1 is transitive as 1 and 2 are related.

G. R6 is not not transitive

I. R4 is not transitive