$($B$3)$ If $B_1,B_2$inB and $B_{1}sube{B}_2,$ then $B_1=B_2.$

Prove that the $f$ "lowing are equivalent for an element $e$ of a matroid:

$($a$)e$ is a loop.

$($b$)e$ is in no bases.

$($c$)e$ is in no independent sets.