All language subtitles for 003 Intersection of Sets_en

Instructor: Welcome back, everyone.

So far, we have only briefly mentioned

how different events can interact with one another.

In this video, we are going to introduce you

to the notion of intersections.

Let's start with the intersection of two events.

When we want both A and B to happen at the same time,

we are talking about their intersection.

Graphically, the intersection is exactly

as the name suggests, the area where these events intersect.

It consists of all the outcomes that are favorable

for both event A and event B simultaneously,

as we denote it as A intersect B.

Let us look at the examples we went over in the last lecture

and see how the intersect changes.

Going back to the first example from last lesson,

the intersection of all hearts

and all diamonds is the empty set.

The empty set has no elements, so there are no outcomes

which satisfy both events simultaneously.

We would write this as A intersect B equals the empty set.

Now you see why we needed this notation.

Let's consider a different example from the same lecture.

The intersection of all diamonds and all queens

is represented by the Queen of Diamonds.

That card is the only one that satisfies being a queen

and being a diamond at the same time,

so nothing else is included in the intersection.

In the example with red cards and diamonds,

the intersection of the two would simply be all diamonds.

That is because any diamond is simultaneously red

and a diamond.

We would write this as A intersect B equals B.

Great job, everybody.

We use intersections only when we want to denote instances

where both events A and B happen simultaneously.

In the next video, we are going to introduce unions.

See you all there.