GO Classes Set Theory And Algebra Practice Set 1 | Question: 19

Question

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?

• A. It is only transitive
• B. It is both antisymmetric and transitive
• C. It is both reflexive and transitive
• D. It has none of those properties

Answer 1

Let $R$ be the relations on a given graph. 

$R=\left\{(0,0) (2,2) (0,1) (1,2) (0,2)\right\}$

• $R$ is not reflexive relation as $(1,1)\notin R$
• $R$ is antisymmetric as $(1,2)\in R,(2,1)\notin R;(0,2)\in R,(2,0)\notin R;(0,1)\in R,(1,0)\notin R$
• $R$ is transitive relations as $(0,1)\in R,(1,2)\in R\rightarrow (0,2)\in R$

Option (B) is correct.