Question $8.$ A map

$f$:$AB$

is said to be an open map if for every open set $U$ of $A,$ the image $f(U)$ is open in $B.$ If $x$ and $Y$ are topological spaces, prove that the projection maps

${}_1$:$xYx,$ and $,{}_2$:$xYY$

are open maps.