Question

Define relations $R_{1}$ and $R_{2}$ on set $A=[2,3,5,7,10]$ as $x R_{1} y$ if $x(y-1)$ and $x R_{2} y$ if $x+y=10$, then the relation $R$ given by $R$ $=R_{1} \cap R_{2}$ is

• A. $\{ \}$
• B. $(3,7)\}$
• C. $\{(3,7),(5,5)\}$
• D. None of these

Answer 1

Answer: (B)

$A=\{2,3,5,7,10\}$
$R_{1}=\{(x, y): x /(y-1)\} $;
$ R_{1} \subseteq A \times A$
and $R_{2}=\{(x, y): x+y=10\} $;
$ R_{2} \subseteq A \times A$
$\Rightarrow R_{1}=\{(2,3),(2,5),(2,7),(3,7),(3,10)\}$
$\quad$ and $R_{2}=\{(3,7),(5,5),(7,3)\} $
$\Rightarrow R=R_{1} \cap R_{2}=\{(3,7)\}$