Question

If the mappings f and g are given by $f=\{(1,2),(3,5),(4,1)\}$ $g=\{(2,3),(5,1),(1,3),\}$then no. of pairs in the mappings $fog$ and $gof$.

Answer 1

If $fϵX\times Y$ and $gϵY\times Z$
Then
$gofϵX\times Z$ i.e
$(x,z)ϵgof$
Applying the above concept, we gives us
$gof=\left\{\right(1,2\left)|\right(2,3),(3,5\left)|\right(5,1),(4,1\left)|\right(1,3\left)\right\}$
$=\left\{\right(1,3),(3,1),(4,3\left)\right\}$
Similarly
$fog=\left\{\right(2,3\left)|\right(3,5),(5,1\left)|\right(1,2),(1,3\left)|\right(3,5\left)\right\}$
$=\left\{\right(2,5),(5,2),(1,5\left)\right\}$
Hence both $fog$ and $gof$ has 3 elements.