Question

Let $R=\left\{\right(1,3),(2,2),(3,2\left)\right\}$ and $S=\left\{\right(2,1),(3,2),(2,3\left)\right\}$ be two relations on set $A=\{1,2,3\}$.Then $R$o$S$ is equal

• A. $\left\{\right(2,3),(3,2),(2,2\left)\right\}$
• B. $\left\{\right(1,3),(2,2),(3,2),(2,1),(2,3\left)\right\}$
• C. $\left\{\right(3,2),(1,3\left)\right\}$
• D. $\left\{\right(2,3),(3,2\left)\right\}$

Answer 1

The correct option is A $\left\{\right(2,3),(3,2),(2,2\left)\right\}$

If $fϵX\times Y$ and $gϵY\times Z$

Then
$gofϵX\times Z$ i.e
$(x,z)ϵgof$

Applying the above concept, we gives us
$RoS=\left\{\right(2,1\left)|\right(1,3),(3,2\left)|\right(2,2),(2,3\left)|\right(3,2\left)\right\}$
$=\left\{\right(2,3),(3,2),(2,2\left)\right\}$