Southbank International School Weblogs

Aim: Sets
A set is an unordered list of objects (which are known as elements). Here is an example of two sets:
{2,3,5,9,1,0}= A
{1,2,4,8,16}= B
The elements of the list do not have to be in any paticular order.
{1,2,3}={3,1,2}
So you could, for example, reorder them from smallest to largest if it helps you.

There are many things we can determine with these sets, such as their intersection (written as n): which means the list of elements that appear in both of those two sets. For example, the elements that appear both in set A and set B, are 1 and 2. This is written as:
AnB={1,2}

There are times where there are no elements which appear in both sets. For example, if:
A= {odd numbers}
B= {even numbers}
In this case AnB is written as:
AnB=empty set OR AnB={}

We can also determine the union of these sets (written as u), which means list all the elements of the two sets. The duplicates are only listed once. So the union of set A and set B would be written as:
AuB={1,2,3,4,5,8,9,16,0}

A universal set is the largest set required to do a problem. At our level, the universal set will always be defined for us.

A complement U, means list all the elements in a universal set (U) and not in set A. It is written as:
$A^1$ or $A^c$
So for example, if:
U={0,1,2,3,4,5,6,7,8}
A={1,3,5,7}
$A^1$ ={0,2,4,6,8}
So, these rules, are always true:
An $A^1$ ={}
Au $A^1$ =U

Sets are commonly shown in venn diagrams:
For example, AnB can be shown as:

The shaded part is the elements in set A that overlaps the elements in set B. In other words, the elements that are both in set A and B

Here is a more complicated example:
$(AnBnC)^1$ can be shown as:

The shaded parts are the elements that do NOT appear in all of the three sets, A, B and C.
That's all on sets!

We spent the rest of the lesson revising some maths terms that we have not looked at in a while. Here are some reminders.

Largest Common factor: the largest number that divides into two numbers.
Least Common multiple: The smallest number that the two numbers divide into.

Natural Number: Counting numbers, positive whole numbers. Ex)1,2,3,4
Integers: All whole numbers including negatives.
Rationals: All numbers that can be written as a ratio of integers.
Real numbers: All numbers including irrationals.
The next presenter is.. whoever hasn't gone yet! =)