Question

9. Let R an equivalence relation. Prove or disprove that R:R is an equivalence relation

Answer 1

ANMSWER:

R is equivalence relation means :

• R is reflexive
• R is symmetric
• R is Transitive

?Let R = { (1,1) , (1,2) , ( 2,1) , (4,1) }

Now R is reflexive because 1R1 , symmetric because 1R1 => 1R1 . R is transitive because 1R1 , 1R2 = > 2R1

Now R' = { (1,1) , (2,1) (1,2) , (1,4) }

Now check its transitivity :

1R2 , 2R1 = > 1R1 thus R' is transitive proved.