Question

Let $A =(1,2,3)$. We define
$R _{1}=\{(1,2),(3,2),(1,3)\}$
$R _{2}=\{(1,3),(3,6),(2,1),(1,2)\} .$
Then, the relation on $A$

• A. $R _{1}$ is relation and $R _{2}$ is not
• B. $R _{1}$ and $R _{2}$ are both is relation
• C. $R _{1}$ and $R _{2}^{2}$ are both non-relation
• D. None of these

Answer 1

Answer: (A)

$R _{1} \subseteq A \times A $.
So , $R _{1}$ is a relation on $A $.
But $(3,6) \in A \times$
A, so $R _{2} \subseteq A \times A$ and
hence $R _{2}$ is not a relation on $A$.
Hence, (a) is the correct answer.