Lesson 2

Lesson 2 Summary

 

Venn diagrams and set notation are two different ways of organizing data to make it more manageable. Venn diagrams can be used to pictorially represent sets and show the relationships between sets. Set notation is used when writing sets of numbers in a more compact way.

 

Both methods are useful. At times, however, one method may be easier to use or preferred.

 

Consider the multiples of 4 in the set of all whole numbers between 0 and 20. This can be described in set notation as {y|y = 4x, 0 ≤ x ≤ 5, x ∈ W}.

 

Using a Venn diagram, it would look like this:

 

Both methods are useful and simple to create in this example.

 

However, if asked to consider the multiples of 4 in the set of all natural numbers between 0 and 1 000 000, set notation again would be fairly simple to create:

 

{y|y = 4x, 0 ≤ x ≤ 250 000, x ∈ W}

 

In this case, a Venn diagram would take a very long time to create if you had to represent all the numbers from 1 to 1 000 000. A Venn diagram would not be a good option for this question.

 

In summary, Venn diagrams can be useful to represent sets of objects easier than set notation, while set notation can be used to represent sets of numbers easier than Venn diagrams. Essentially, they both show the same thing; however, the situations you encounter will determine what better describes the sets you are given.

 

In the next lesson you will continue to build on set notation and Venn diagrams by applying them to contextual problems.