Question

Let $R=\left\{\right(1,3),(4,2),(2,3),(3,1\left)\right\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is

• A. a function
• B. reflexive
• C. not symmetric
• D. transitive

Answer 1

Answer: (A), (C)

The correct options are
A a function
C not symmetric

$R=\left\{\right(1,3),(4,2),(2,3),(3,1\left)\right\}$
$A=\{1,2,3,4\}$
Every element of $A$ is related to one and only one element. So the given relation is a function.
For a reflexive relation, every element should be related to itself, which is not the case for the given relation. Hence not reflexive.
Since $(2,3)\in R$ but $(3,2)\notin R$.
Hence, $R$ is not symmetric (symmetric condition $aRb\Rightarrow bRa$)
$(4,2)\in R$, $(2,3)\in R$, but $(4,3)\notin R$. Hence not transitive.