Tip:
Highlight text to annotate it
X
>> Hi, this is Julie Harland
and I'm YourMathGal.
Please visit my website
at yourmathgal.com
where you could search for any
of my videos organized
by topic.
This is part 4 of steps
and we're going
to problems involving more
than one step.
In this video, we're going
to use just
for the universal set,
the numbers from 1 to 9.
And we've got 3 subsets A,
B and C defined as following,
and we're then we're going
to do the following
4 problems.
Here's the first problem.
Find B complement minus a
union C. Now remember,
this is not regular
subtraction,
this is the difference
operation right?
It's the difference of 2 sets,
a little bit different.
So B complement,
what is that mean?
That means,
everything
in the universal set except B,
the elements in B.
So everything except 4,
5 and 7.
Well B, 1, 2, 3, 6,
8 and 9 minus,
okay why don't you figure this
part out.
What's a union C?
Write that down.
That means we're joining
together all the elements in A
or C. So if it's a list
and one of them,
it gets in the union.
So I have all the elements
of A, 1, 4, 7 and 8.
And also anything
in C gets fit in,
so I have a 2.
I already have a 7 in here,
so I don't write
down again, and a 9.
And now, what do I do.
So remember,
you want anything left
in this per set right,
which is B complement that's
not over here on the right.
So let's see.
Do I get to keep the 1?
No, because there's a 1
over there.
I get to keep the 2?
No, because there's a 2
over there.
Do I get to keep the 3?
Yes. Do I get to keep the 6?
Yes. Do I get to keep the 8?
No, because there's an 8
over there and I don't get
to keep the 9.
So finally answer here is
what's left is only 3 and 6.
All right.
Here is the second problem.
Why don't you go ahead
and put the video on pause
and try this
on your own first.
All right so we have
to do A intersect
to able be begin with.
Right, so we look at sets A
and B and their intersection
is whatever elements they have
in common.
And they have a 4 and a 7
in common.
So that's 4 and 7,
I'm going to union that,
put the A,
take away C. All right.
So that's a little complicate
to do in your head
but maybe you could do it.
If you over here at A,
we've got 1, 4, 7 and 8 or any
of those over in C. I've got
2, 7, and 9.
Well, there's a 7,
so I can't keep the 7 in A.
So what's left would be the 1,
4, and 8.
If you want, you could write
down what A is, right?
And say I got
to take the 7 out.
Right, that's a sort
of like scratch work
over here.
And now I want take the union
of these 2 sets.
So what numbers are left?
Well they have a 4 in common,
but all the rest
of them were unique numbers.
So I have the 1, the 4,
the 7 and the 8.
It doesn't matter
where you put the
numbers right.
I could put 4, 7, 1, 8.
It doesn't matter as long
if you use my braces,
my commas to separate
the numbers.
All right,
here's the next one.
Same universal set,
same 3 subsets.
C, well that's easy
to do isn't it?
But I'm going to have
to do a couple of things
over here.
I should do the A union B
and take the complement.
First over now, I'm not going
to write this just
to make it a little
bit easier.
And let's write it what A
union B is
to begin with, okay.
So A union B, if you look
between these 2 sets,
that's in A or B,
it gets in the union,
so I get all of A, 1, 4,
7 and 8, and all of B
which is 4, 5, and 7.
We'll I've got a 4 already,
5 I don't have yet.
And I have a 7 already.
All right,
so there in this set,
those 5 elements for a union A
and B. And now I've take the
complement of that okay?
Now I'm going to ahead
and write down with the,
what's in C right now.
That's 2, 7 and 9.
And what's the complement
of this set 1, 4, 7, 8 and 5,
everything
in the universal set except
those 5 numbers.
So what's left?
2, 3, there's a 5 how
about a 6 and a 9.
All right those are all the
numbers in the universal set
that are not 1, 4, 7, 8 or 5.
Last step, so now we're have
to do the set difference.
So let's see what could do,
we get to keep
from this first set.
All right can I keep the 2?
No, because there's 2
over here,
so you'll take that out.
The 7, there's no 7
over there,
so I can keep the 7,
9 I have to take that out
because of that 9.
So our final answer will only
have a 7 inside the set.
So there's the answer.
Last one, again, try this one
on your own,
make sure you do what's
in parenthesis first,
then take the complement
and then subtract that.
So put the video on pause
to give yourself time
to do this.
All right so lets see,
we're going
to do B intersect C.
So I'm going
to write what B intersect
C is.
I'm going to look
at these 2 sets, B and C
and do they have any elements
in common?
Only a 7. So that's only 7.
And I could write out all of A
but I know I'm going
to do one more steps,
I'm save myself some extra
writing and do
that the following step.
Now that I've take the
complement of this set,
it only contains 7.
Well that's every number
from 1 to 9 except 7.
[ Pause ]
Right, that's the complement
of this set that contains 7.
And subtract anything
out what's in A, and A is 1,
4, 7 and 8.
So what do I have to take
out of here?
Does the 1 get to stay in?
No 'cause there's the 1
over here.
Does the 2 get to stay in?
Yes. Does the 3 get
to stay in?
Yes. How about the 4?
No, 'cause there's a 4
over there.
5 gets to stay in,
6 gets to stay in.
8? No, 'cause there's 8
over there
so like it's taken out.
9 gets to stay in.
So what's left here 2, 3,
5, 6 and 9.
And there we've got.
All right, so we've done--
I've done 5 videos on set C,
so using the set notation.
And we've only been doing sets
where we can actually write
the universal set.
So another words,
it's a finite number
of elements in each set.
And I'm going to video
on venn diagrams,
so if you want
to know a little bit more
about sets, then you want
to go on to the next video
on venn diagrams.
[ Pause ]
Please visit my website
at yourmathgal.com
where you can view all
of my videos
which are organized by topic.