First, mathematics usually considers lower- and uppercase variables to be different symbols. For example, x ∈ X is often used for a set X and its element x. Therefore, I suggest using same-case letters for all sets unless the textbook or lecture notes strongly suggest otherwise.

Strictly speaking, all the sets r, c, m and v are sets of numbers, not vehicles. So, v ∩ m is the set of registration numbers of old motorcycles.

I am not sure what you mean by "they," but if two sets intersect, they are not necessarily the same.

No, draw some Venn diagrams.

Why do you use M here since the question talks about cars, not motorcycles? Also, if you use union, then youaddsomething to old vehicles while the questionimposes a restrictionon the set of all vehicles. You should use intersection or set difference.

This is the set of old cars andallmotorcycles while you need onlynewmotorcycles.