Tip:
Highlight text to annotate it
X
(male narrator) So we actually already did this a little earlier,
but I'm gonna do it again.
Here, we're gonna create Venn diagrams
to illustrate A union B, A intersect B,
and A complement intersect B.
Now a Venn diagram is, uh...a diagram created
by using overlapping circles,
so I'll have a circle for Set A and a separate circle for Set B.
Uh...and then there's an overlap or potentially an overlap
between those two sets.
So A union B... so A union B
is gonna contain everything from Set A
and everything from Set B.
Uh...so we'll either outline it like that,
or we could shade it in.
And that whole shaded region there is A union B.
Now if, again, we have Sets A and B,
and we want A intersect B...
these are the elements that are in both sets.
So this would be only this little region here.
Those are the valleys
that are both in Set A and in Set B.
Finally...for our last one here,
we've got A complement intersect B,
so again, remember, A complement
means everything that's not in A.
So we're outside of Set A...
but we're inside of Set B.
So it's everything that's inside Set B
that's not in Set A,
and so it's...that would be this region there.
So let's look at one more now--
uh...a slightly more complicated one
using a Venn diagram to illustrate this intersection.
So now here, we have three sets,
so we're gonna need 1...2...uh...3 different...sets
going on here-- all overlapping.
And it's pretty hard to work with more than three sets
with Venn diagrams.
It is possible,
but we'll limit ourselves to three.
So let's start with...H intersect F.
So remember, H intersect F is...was this region here.
Right?
It was this area that was in both H and F.
Now we want the intersection of, uh...no...
so now we need the complement of that set.
So the complement of...the complement of that set
would be everything outside
of...that little...that little football-shaped region.
So we don't want that part.
We want everything outside of it.
Now we need the intersection between that and W.
So we need everything in W.
We need everything in W here
that's not in that little football-shaped region.
So that's gonna be, uh... everything down here is fine.
Everything over here is fine.
Everything over here is fine.
The part that we don't want is this part here.
So altogether, we're gonna have...oop, sorry.
[humming]
We're gonna have that whole region there as...as that set.