Consider the poset $\{$a$,$ b$,$ c$,$ d$,$ e$,$ f$,$ g$,$ h$\},$ with the relation

$\{($a$,$ e$),($b$,$ d$),($b$,$ f $),($c$,$ a$),($d$,$ c$),($d$,$ h$),($f$,$ c$),($g$,$ b$),($h$,$ a$)\}.$

$1.$ Use the topological sort algorithm $($of text$)$ to obtain a sorted order of these

elements that is consistent with the given partial order. Give some details

$($but not too much!$)$

$2.$ Is the sequence $($gbf cdhae$)$ consistent with the given partial order? Why?

$1$