Start Screen If this is your first time using this program, click the first place ribbon. Otherwise,...

Start ScreenIf this is your first time using this program, click the first place ribbon.

Otherwise, click a box below to go to a certain part of the investigation. If you choose the wrong one, click on the house icon to go back to this page.

Go to part 2 Go to part 3 Go to part 4

Click on Sherlock Holmes to begin

the investigation!

Section 7.3

To continue the investigation, click on

Sherlock Holmes.

If you don’t know a word or symbol that is highlighted,

click on it to see a definition!

Set

Who is Sherlock Holmes???

Click Me!Don’t forget! Click on the house to start over!

Directions…

In a class of 30 students, 17 watch MTV and 12 play video games.

5 students watch MTV and play video games. See if you can answer the following 4 questions:

1. How many students watch MTV but do not play video games?

717

24 12

6

30

Almost…

Later I will help you learn to use a tool that will help you investigate these kinds of questions. Try the next question…


5 students watch MTV and play video games.

2. How many students play video games but do not watch MTV?

717

24 12

6

30

Almost…




3. How many students watch MTV or play video games (possibly both)?

717

24 12

6

30

Almost…




4. How many students neither watch MTV nor play video games?

717

24 12

6

30

Almost…

Let’s learn a way to investigate these types of

questions that people in the business world use.

Notation

First some set notation symbols.

Assume that A is the set of even natural numbers between 1 and 10 inclusive.

There are 5 elements in set A:

A = {2,4,6,8,10}

Another way to say this is #(A) = 5

Think of it as saying…

# (A) = 5

the number of elements in set A equals 5

Let U be the set of all students in the class.

Let M be the set of students who watch MTV.

Let G be the set of students who play video games.

We know that #(U) = 30.

We know that #(M) = 17.

We know that #(G) = 12.

Let U be the set of all students in the class.

Let M be the set of students who watch MTV.

Let G be the set of students who play video games.

We know that #(U) = 30.

We know that #(M) = 17.

We know that #(G) = 12.

M G

U

M G

We know that #(U) = 30, #(M) = 17, and #(G) = 12.

Think of ALL the students in the class being represented by points inside the rectangle U.

U

M G


Inside circle M are the 17 students who watch MTV.

U

M G


Inside the circle M are the 17 students who watch MTV.

Inside circle G are the 12 students who play video games.

U

M G


Inside the circle M are the 17 students who watch MTV. Inside the circle G are the 12 students who play video games.

The 5 students who watch MTV and play video games are in the region inside both circles which is colored green.

U

M G


The green region (5 students) is denoted by

M G, which is read, “M intersect G”

or “the intersection of M and G.”

U

M G


Moreover, #(M G) = 5

5

The green region (5 students) is denoted by



U

M G


Let’s have a quick review,

how do you say the following:

5

M G

A) “the intersection of M and G”B) “M intersect G”

C) “M and G together”D) both choices A & B

Great Job!

A mnemonic device for remembering that the symbol means intersection,

is thinking that the symbol

looks like the letter nn for

inntersection!

U

M G


5

And remember that the green region has 5 students in it, who

watch MTV and play video games, which is #(M G) = 5So if circle M has 17 in all, but 5 of them are in the intersection area, how many are in just the blue area?

17

2212

27

U

M G


5

What about the yellow area?

If circle G has 12 total, how many are in just

the yellow area?7

1224

17

We also know that #(M G) = 5

1212

U

M G

5

So now we have all three areas filled in!

1212 77

Let’s try those questions from the start of the investigation one more time...

U

M G

5

How many students watch MTV only, no video games?

1212 77

512 17724 6

U

M G

5

How many students play video games only, no MTV?

1212 77

512 17724 6

U

M G

5

How many students play video games or watch MTV (possibly both)?

1212 77

512 17724 6

U

M G

5

Our three regions add to 24.

The 24 are all the students who play MTV or play video games (or both!)

1212 77

1212 ++ 55 ++ 77 == 2424

U

M G

51212 77

We have a symbol in math that describes this joining of

regions. It is called union and looks like the letter UU.

So M G is the union of sets M and G.

Think U U for Union!

U

M G


5

What about the white area inside the box?

Use the information at the top of this page to come up with a guess…then click on Sherlock to try the question on the next page…

We also know that #(M G) = 5 and #(M G) = 24

1212 77

U

M G

5

How many students neither play video games nor watch MTV ?

1212 77

512 17724 6

U

M G

5

Right! There will be 6 students who don’t play video games or watch MTV, but are still part of the class, which is set U,

with 30 students total.

Those 6 go in the white space.

1212 77

6

Now click on the link below to play a game online that will test how well you understand Venn Diagrams.

You may see some symbols you don’t know, and you may see more than 1 circle!

This will be an exciting challenge! You can play this till it’s time to go!

http://nlvm.usu.edu/en/nav/frames_asid_153_g_4_t_1.html?open=instructions

http://nlvm.usu.edu/en/nav/frames_asid_153_g_4_t_1.html?open=instructions

Almost! Let’s look at the information from the previous screen again.

GO BACK

Moreover, #(M G) = 5

The 5 students in this green region is denoted



Almost! Let’s take another look…

GO BACK

U

M G

5

Circle M, the blue and green area, has 17.

Now subtract out the 5 students who are already in there, inside the intersection area.

Not including the 5 in the green area, how many are in just the blue area?

GO BACK

U

M G

5

Circle G, the yellow and green area, has 12.

Now subtract out the 5 students who are already in there, inside the intersection area.

Not including the 5 in the green area, how many are in just the yellow area?

1212



GO BACK

U

M G

5

The whole class has 30 students, so how many are not represented in the diagram so far?

1212 77

#(U) = 30,

#(M) = 17

#(G) = 12.

#(M G) = 5


GO BACK

U

M G

51212 77

Remember:

Circle M has the students who watch MTV

Circle G has the students who play video games

The overlapping region has the students who play video games and watch MTV.

Set

A collection of objects.

Example: The set of all even natural numbers less than 10 is {2, 4, 6, 8}

GO BACK

Mnemonic Device

A tool for remembering information easily, it can be a

rhyme, song picture, or acronym.

Example: A mnemonic device for remembering to spell dessert with two s’s, is to think of the dessert

Strawberry Shortcake

GO BACK

Remember…

U = the set of all students in the class

M = the set of students who watch MTV

G = the set of students who watch MTV

GO BACK

Remember…

means intersection,

or the overlapping of two sets.

GO BACK

Remember…

means union,

or the joining together of two sets.

GO BACK

Sherlock Holmes Info Page

From the websitehttp://www.crimelibrary.com/gangsters_outlaws/cops_others/sherlock_holmes/1.html

In a sea of fictional detectives that includes the greats, the near-greats, and a great many wannabes, the lighthouse that shines above them all is, of course, Sherlock Holmes. Created by Sir Arthur Conan Doyle and presented through the narration of the fictional Dr. Watson, Holmes is the most brilliant detective ever. His powers of observation seem supernatural until he utters the famous phrase, “Elementary, my dear Watson,” and proceeds to enumerate the logical steps that have brought him to a prescient conclusion. The most innocuous detail can lead Holmes to profound revelations.

GO BACK

Click on Peter!

U

M G

51212 77

There is another way to refer to the students who JUST watch MTV or JUST play video games. We use subtraction!

The blue area, MTV only students, is the same as M-G, because all of circle G, the green and yellow areas, gets subtracted out.

Same thing with the yellow area, video game only students.

It is the same as G-M.

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