Question

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

Answer 1

If $fϵX\times Y$ and $gϵY\times Z$
Then
$gofϵX\times Z$ i.e
$(x,z)ϵgof$
Therefore
$fog=\left\{\right(2,3\left)|\right(3,5),(1,3\left)|\right(3,5),(5,1\left)|\right(1,2\left)\right\}$
$=\left\{\right(2,5),(1,5),(5,2\left)\right\}$
Hence
$fog\left(1\right)=5$