X$.$ Which statement$($s$)$ is$/$are true of acid$-$catalyzed alcohol dehydrations?

a$.$ Protonation of the alcohol is a fast step.

b$.$ Formation of a carbocation from the protonated alcohol is a slow step.

c$.$ Rearrangements of less stable carbocations to more stable carbocations are common.

d$.$ Loss of a proton by the carbocation intermediate is a fast step.

e$.$ All of these choices.