Math: Sets and Venn Diagrams
1. The Genesis
Today we will talk about Sets and Venn Diagrams.
The cardinal number of the universal set is 10. We write this down as:
A. |A|=3
B. #A=3
C. n{U}=10
The number of elements in a set is called a cardinal number. (You may be wondering what our elements are. they're just a bunch of Greek letters acting high and mighty because they're all the rage in the World of Math.)
Here comes our example sets and their lovely cardinal numbers.
2. The Medietas: Subsets and Proper Subsets
And now we get to learn about Subsets and Proper Subsets (this is still a part of Sets and Venn Diagrams).
subset: D β A
proper subset: A β D
D is a subset of A because the elements of D are also in A. However, in A β D, A is a proper subset of D because not all of A's elements are in D. But if they were to merge, they would both have to same cardinal number and elements and we end up with a...
Equal Set:
An equal set is made up of 2 or more sets that have the same cardinal number & elements regardless of order. Let's take a look at our example sets:
Yes, we are "gazing and gaping" at all of you trying to find an equal set. Have you found any?
Wow, you're too smart. You don't need to learn this.
Well, anyway we can see why they're equal sets. Good job! But what are...
Equivalent Sets (?):
In hearing "equal and equivalent," they seem to mean the same thing don't they? No, not at all. Equivalent sets mean that they have the same cardinal number but not the same elements. Can you spot any here?
All righto mate!
Well at least we got a little test to see if they're cheating or not.
Ok, so what does this mean?
No it's not the universal set symbol again. It's stands for union. This happens when we add, or merge two sets (D and E). But of course it doesn't mean that they're getting married.
Wow, congrats! Can you please tell us your love story?
Oh yes right we don't have time for that. So let's continue to the...
Complement (opposing elements):
No not compliment, complement. This happens when we pick the opposite elements of a set based on the universal set. Let's pick U, A, and B for this one.
Okay here goes!
Yes she is, but let's get on with this guys, don't want to keep the audience waiting, 'specially ladies (like me).
If we look at the universal set we notice that B has half its elements and also the opposite elements of A. So we can say that B is also a complement of A.
An empty set symbol: Ο or Ο The phi (pronounced fly) and we'll find out more about this in...
Post-Medietas (PM): The Intersection of two sets and the Venn Diagram
The goal of the Venn Diagram (created by Joseph Venn) and the intersection (β©) is to show the similarities between two sets or more, take for example...
And now our Venn Diagram is ready!
And that's it everyone! Till next time! Bye!
FINIS
Comments