GO Classes Set Theory And Algebra Practice Set 1 | Question: 18

Question

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

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

Answer 1

From the given digraph following elements in the relation $R=\left \{ (0,0),(1,1),(2,2),(0,2),(1,2),(2,1),(0,1)\right \}$

• Relation $R$ is reflexive as all the diagonal elements are there; each node having self-loops.
• Relation $R$ is not symmetric as for each pair $a^Rb$ there should be $b^Ra$, (0,2) is there but (2,0) is not present.
• Relation $R$ is not antisymmetric as $(1,2),(2,1)$ both pair present in the set.