Currently doing a short maths course to aid and help in 3d modeling and animation,just wondering if anyone could help in set theory?

The questions were as follows and my answers too.

[A]

Given the following sets: r =the set of registration numbers of all vehi-

cles (i.e. Consider r as the type or Universe for this problem), c =the set of

car registration numbers, m =the set of motorcycle registration numbers,

and V =the set of registration numbers of old Vehicles

Describe the following in words e.g. m (intersection) V = the set of all old motorcylces.

(i) (V(union)m);

The set of old vehicles and all registration numbers

(ii) (V (intersection) (cnr))(symmetric difference) c;

The set of car registration numbers

Write down the following sets using set notation

(iii) the set of new vehicles that aren't a motorcycle;

(r(symmetric difference)c)(union)V

(iv) the set of all vehicles that are a car or are an old motorcycle

(c\r)(union)(m(intersection)V)

[B]

Considering any 4 subsets of a universe, U, work out (and show your

working)

(v) how many different regions there could be.

8 different regions

(vi) how many dffierent ways of combining these regions using boolean combinations are there?

256 of combining these

[C]

(vii) Decide and state whether any subset of a countable set is itself

countable. Explain your answer in your own words.

Thats it guys, sorry to drag it out also Rather then using set notation I have used words in brackets cause everytime I tried to copy and paste it came out with something completly different. Thnaks in advance ** **