Consider the set A $=\{$a$,$ b$,$ c$,$ d$,$ e$,$ f$,$ g$\}.$ For each of the following collections of subsets of A decide if it is a partition of A$,$ and if it is not explain why?

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

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

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

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