Set Theory, Venn Diagrams & Exclusive Events

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  • 0:01 Sets
  • 0:41 Venn Diagrams
  • 1:52 Mutually and…
  • 2:53 Putting It All Together
  • 3:52 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

In this lesson, we're going to go over the concepts of sets and Venn diagrams, as well mutually exclusive and non-mutually exclusive events in terms of how they all tie in together.

Sets

Do you have a collection of things at home, a set? Sure you do! I bet you have a sets of things like video games, or dolls, or books. You can also have a set of different numbers.

A set is written inside of curly brackets, so a set of integers is written as {0, 1, 2, 3, 4, 5, ...} in brackets, and a set of something like video games can be written as {mario kart, gta v, fifa 2016, minecraft, tetris, ...}, again all of that in brackets of course.

Let's see how sets apply to Venn diagrams as well as mutually and non-mutually exclusive events.

Venn Diagrams

Venn diagrams are quite simply visual representations of sets. I'm sure you've seen them, it's those famous overlapping circles.

Let's say you have a set of pets at home. They are {dolly, libby, chessee, topaz, kitty, buck}. Because we are dealing with mathematical concepts, as opposed to English class, each pet is considered an element of the set and is not capitalized. The pets, or elements, that like canned food are {dolly, libby, chessee}. The pets that like kibble are {topaz, kitty, buck}.

In other words: canned food = {dolly, libby, chessee} and kibble = {topaz, kitty, buck}.

We can put their names into a separate circle and label each circles as either canned food or kibble, appropriately.

Now if we take those to circles and bring them together to have an area in the middle where they intersect, we create the possibility that some of the these pets may like both canned food and kibble and not just canned food or kibble. Let's say {dolly, topaz} likes canned food and kibble. Because they like both, they would then be placed in the intersection of the Venn diagram.

Mutually and Non-Mutually Exclusive Events

Let's take this basic knowledge or sets and Venn diagrams a bit further, to understand how they relate to mutually exclusive and non-mutually exclusive events.

Take out a standard deck of 52 playing cards, this our set - the playing cards. Turn the set of cards so that you can see the value of the cards. If I ask you to scan throughout the deck, and to pull out an ace or a king I'm asking you about mutually exclusive events, events that cannot occur at the same time. Meaning you can only pull out an ace or a king, not both.

Another example of mutually exclusive events is landing a coin on either head or tails, after flipping it. You can't land on both at the same time.

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