Question

Let $A=\{1,2,3,4\}$ and $R$ be a relation in $A$ given by $R=\left\{\right(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,1),(1,3\left)\right\}$ then identify the relation $R$.

• A. reflexive
• B. symmetric
• C. transitive
• D. an equivalence relation

Answer 1

Answer: (A), (B)

reflexive
symmetric

Let $A=\{1,2,3,4\}$ and $R$ be a relation on $A$ given by $R=\left\{\right(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,1),(1,3\left)\right\}$.

Now for all $1,2,3,4\in A$, $(1,1),(2,2),(3,3),(4,4)\in R$, this gives the relation $R$ is reflexive.

Again for $(1,2)\in R\Rightarrow (2,1)\in R$ and $(1,3)\in R\Rightarrow (3,1)\in R$ for $1,2\in A$. This gives the relation $R$ is symmetric.

But the relation is not transitive as $(2,1),(1,3)\in R$ but $(2,3)\notin R$.

Hence the relation is not equivalance.