GO Classes Set Theory And Algebra Practice Set 1 | Question: 17

Question

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

• A. It is both symmetric and transitive
• B. It is both reflexive and transitive
• C. It is reflexive, antisymmetric, and transitive
• D. It is both reflexive and antisymmetric

Answer 1

It is both reflexive and transitive.

Answer 2

From the given graph we can determine the relation $R$ as :

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

• $R$ is reflexive relation as all digonal pair is present in relation.
• $R$ is not symmetric as $(0,2)\in R,(2,0)\notin R; (2,1)\in R, (1,2)\notin R$
• $R$ is not transitive relation as $(0,2) (2,1)\rightarrow (0,1)\notin R$,similarly $(2,1) (1,0)\rightarrow (2,0)\notin R$ 
• $R$ is antisymmetric relation as $(0,2)\in R(2,0) \notin R$; similarly $(2,1)\in R(1,2) \notin R$