If the mappings $f$ and $g$ are given by
$f = \{ (1,2),(3,5),(4,1)\}$ and $g = \{ (2,3),(5,1),(1,3)\}$, write $fog$.

It is given that,, $f = \{ (1,2),(3,5),(4,1)\}$

and $g = \{ (2,3),(5,1),(1,3)\}$

Now, $fog(2) = f\{ g(2)\} = f(3) = 5$

$fog(5) = f\{ g(5)\} = f(1) = 2$

${\mathop{\rm fog}\nolimits} (1) = f\{ g(1)\} = f(3) = 5$

$fog = \{ (2,5),(5,2),(1,5)\}$