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.