Question

Let $A=\{1,2,3\}$ and $R=\{(1,2),(2,3),(1,3)\}$ be a relation on $A$. Then $R$ is

• A. neither reflexive nor transitive
• B. neither symmetric nor transitive
• C. transitive
• D. none of these

Answer 1

The correct option is C transitive

The given relation is not reflexive as $(1,1),(2,2),(3,3)\notin R$.

Again the relation is not symmetric as $(1,2)\in R$ but $(2,1)\notin R$.

But the relation is transitive as $(1,2)\in R,(2,3)\in R\Rightarrow (1,2)\in R$ for all $1,2,3\in A$.