Thread: Set notation theory?

Hi folks, doing a short part time 3D modeling course and I am stumped. Never done this before but i had a crack at it anyway. To be honest I'm absolutely confused.

So it goes like this:
Given the following sets: r =the set of registration numbers of all
vehicles (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 (intersects) V = the set of all old motorcylces

(V (Intersects) m)
The set of all old motorcycles
(as far as i know they are the same if they intersect?)

(V (Union) (r\m)) (symmetric Difference) c
The set of all motorcycles

Write down the following sets using set notation:
the set of old vehicles that aren't a car
(V (union) (R\M))

the set of all vehicles that are an old car or are a new motorcycle
(M (union) (C (intersects) V))

not asking for answers, just guidance if im going the right way.

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.

Originally Posted by oldman1

(V (Intersects) m)
The set of all old motorcycles

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.

Originally Posted by oldman1

(as far as i know they are the same if they intersect?)

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

Originally Posted by oldman1

[/B](V (Union) (r\m)) (symmetric Difference) c
The set of all motorcycles

No, draw some Venn diagrams.

Originally Posted by oldman1

Write down the following sets using set notation:
the set of old vehicles that aren't a car
(V (union) (R\M))

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

Originally Posted by oldman1

the set of all vehicles that are an old car or are a new motorcycle
(M (union) (C (intersects) V))

This is the set of old cars and all motorcycles while you need only new motorcycles.

Thank you for the response. I think it has helped!

heres my re-attempt.
1: Set of reg numbers of old motorcycles
2: set of reg numbers for old cars
3: (V n (r\c))
4m (symmetric difference) (c n V))

Was that any better?

Like i say first time doing this so i had to learn what you meant by venn diagram!
Thanks for your time

Originally Posted by oldman1

1: Set of reg numbers of old motorcycles

Correct.

Originally Posted by oldman1

2: set of reg numbers for old cars

Could you explain your reasoning?

I used capital letters to denote sets in the following picture. We are talking about .



On the left, the set is hatched using north-east lines and C is hatched using north-west lines. The former set is everything except motorcycles plus old vehicles, i.e., everything except new motorcycles. To form the symmetric difference, we must take the union of and C and subtract their intersection. Since C is a subset of , the union is and the intersection (double-hatched) is C. Subtracting C, we get the set on the right.

Originally Posted by oldman1

3: (V n (r\c))

Yes. If r is indeed the universal set, then this is the same as v \ c.

Originally Posted by oldman1

4: (m (symmetric difference) (c n V))

Why symmetric difference? Symmetric difference corresponds to "exclusive or": either an old car or a new motorcycle, but not both. Union corresponds to regular, "inclusive or": an old car or a new motorcycle, maybe both. In this particular situation, symmetric difference and union give the same result because the sets of cars and motorcycles are disjoint. However, using symmetric difference to represent regular "or" may lead to unnecessary head scratching.

More important, as I have already said, you refer to all motorcycles instead of just to new ones.