Set Notation Help

glenn101 · 2008-12-20 18:08:35

Hi everyone, I'm just getting confused with several questions related to set notation, and set notation is something I have to know perfectly to score well this year, any help for this post would be much appreciated.

Can you please explain how you derive your answers.
1. For A={1,2,3,4,5,6,7,8,9,10}, B={2,4,6,8,10} and C={1,3,6,9}, find;
A\(B intersect C)=...

This question I don't understand at all, its not making any sense to me.
For each of the following, use one number line on which to represent the sets;
a) [-3,6], [2,4], [-3,6] intersect [2,4]
b) [-3,6], R\[-3,6]
c) [-2,∞), (-∞,6], [-2,∞) intersect (-∞,6]
d) (-8,-2), R(minus)\(-8,-2)

Thanks very much in advance,
Glenn.
Note: I still need help with this, I still am having trouble.

Last edited by glenn101 (2008-12-21 14:02:39)

mathsyperson · 2008-12-22 00:38:15

The \ symbol (sometimes spoken as "less") is placed between two sets and it makes the set of elements that are in the first set but not the second.

eg. {1,2,3} \ {1} = {2,3}

I think this can only be used when the second set is a subset of the first, I've never seen it when that hasn't happened.

In your question, the only element shared by B and C is 6, and so A \ (B intersect C) is given by {1,2,3,4,5,7,8,9,10}

The second question uses intervals, which represent a section of a number line.
eg. [3,6] is all the numbers between 3 and 6, inclusive.
Note that this is different from {3,4,5,6}, because the interval contains all numbers (like 3.7 or π) instead of just the whole ones.
Now that you know that, you should be able to answer the questions in a similar way to the first one.

Some more things you'll need:

Round brackets also mean intervals, but they don't include the end-points.
So (3,6) is the numbers between 3 and 6 but not including 3 or 6.
You can also have (3,6] or [3,6) if you want to include one end-point but not the other.

R is the set of all numbers. Another way of saying it would be (-∞,∞).
Similarly, R(minus) is the set of all negative numbers, ie. (-∞,0).

glenn101 · 2008-12-22 12:36:23

Thanks so much mathsyperson, you couldn't have explained it any better.
Thats exactly what I needed, just needed clarification on certain things which you have provided.
Many thanks mate:)
oh as a side note.
can \ be reffered to as (not) that works for me some times.
Actually I thank that is true as I have seen R/{0} meaning R excluding 0 correct?

Last edited by glenn101 (2008-12-22 13:01:05)

mathsyperson · 2008-12-22 13:17:05

It should be a backslash, but you're right in what it means.
That set pops up fairly often, such as when dealing with functions like 1/x.
It's defined everywhere except x=0, so it's defined on R\{0}.

Math Is Fun Forum

#1 2008-12-20 18:08:35

Set Notation Help

#2 2008-12-22 00:38:15

Re: Set Notation Help

#3 2008-12-22 12:36:23

Re: Set Notation Help

#4 2008-12-22 13:17:05

Re: Set Notation Help

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