Sets n Ven Diagram

Sets and Venn Diagrams part II

Sets

 

A set is a collection of things.
For example, the items you wear is a set: these would include shoes, socks, hat, shirt, pants, and so on.
You write sets inside curly brackets like this:
{socks, shoes, pants, watches, shirts, ...}
You can also have sets of numbers:

• Set of whole numbers: {0, 1, 2, 3, ...}
• Set of prime numbers: {2, 3, 5, 7, 11, 13, 17, ...}

Ten Best Friends

You could have a set made up of your ten best friends:

• {alex wong, tony blair, john casey, honey dew, erin malik, francis , glen, huntera, irah, jade}

Each friend is an "element" (or "member") of the set (it is normal to use lowercase letters for them.)


Now let's say that alex wong, john casey, honey dew and huntera play Soccer:

Soccer = {alex wong, john casey, honey dew, huntera}

(The Set "Soccer" is made up of the elements alex wong, john casey, honey dew and huntera).

And casey, drew and jade play Tennis:

Tennis = {casey, drew, jade}

You could put their names in two separate circles:

 

Union

You can now list your friends that play Soccer OR Tennis.
This is called a "Union" of sets and has the special symbol ∪:

Soccer ∪ Tennis = {alex wong, john casey,honey dew, huntera, jade}

Not everyone is in that set ... only your friends that play Soccer or Tennis (or both).
We can also put it in a "Venn Diagram":

Venn Diagram: Union of 2 Sets

A Venn Diagram is clever because it shows lots of information:

• Do you see that alex, casey, drew and hunter are in the "Soccer" set?
• And that casey, drew and jade are in the "Tennis" set?
• And here is the clever thing: casey and drew are in BOTH sets!

Intersection

"Intersection" is when you have to be in BOTH sets.
In our case that means they play both Soccer AND Tennis ... which is casey and drew.
The special symbol for Intersection is an upside down "U" like this: ∩
And this is how we write it down:

Soccer ∩ Tennis = {casey, drew}

In a Venn Diagram:

Venn Diagram: Intersection of 2 Sets

 this is the video

Which Way Does That "U" Go?

 

Think of them as "cups": ∪ would hold more water than ∩, right?
So Union ∪ is the one with more elements than Intersection ∩

Difference

You can also "subtract" one of the set from another.
For example, taking Soccer and subtracting Tennis means people that play Soccer but NOT Tennis ... which is alex wong and huntera.
And this is how we write it down:

Soccer − Tennis = {alex wong, huntera}

In a Venn Diagram:

Venn Diagram: Difference of 2 Sets