If $f = \{ (1,2),(3,5),(4,1)\}$ and $g = \{ (2,3),(5,1),(1,3)\} ,$ then $$gof$$ $= \ldots \ldots \ldots$ and $fog = \ldots \ldots \ldots ..$

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

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

$gof(1) = g\{ f(1)\} = g(2) = 3$

$gof(3) = g\{ f(3)\} = g(5) = 1$

$gof(4) = g\{ f(4)\} = g(1) = 3$

$gof = \{ (1,3),(3,1),(4,3)\}$

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

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

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

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