Start Screen If 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 2Go to part 3Go 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?

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

In a class of 30 students, 17 watch MTV and 12 play video games. 5 students watch MTV and play video games. 2. How many students play video games but do not watch MTV?

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

In a class of 30 students, 17 watch MTV and 12 play video games. 5 students watch MTV and play video games. 3. How many students watch MTV or play video games (possibly both)?

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

In a class of 30 students, 17 watch MTV and 12 play video games. 5 students watch MTV and play video games. 4. How many students neither watch MTV nor play video games?

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 We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG Inside circle M are the 17 students who watch MTV.

U M G We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG 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 We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG 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 We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG 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 We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG Moreover, #(M G) = 5 5 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 We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG 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,mnemonic device is thinking that the symbol n looks like the letter n for n i n tersection!

U M G We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG 5 And remember that the green region has 5 students in it, who watch MTV and play video games, which is #(M G) = 5 So if circle M has 17 in all, but 5 of them are in the intersection area, how many are in just the blue area?

U M G We know that #(U) = 30, #(M) = 17, and #(G) = 12.UMG 5 What about the yellow area? If circle G has 12 total, how many are in just the yellow area? We also know that #(M G) = 5 12

U M G 5 So now we have all three areas filled in! 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?

U M G 5 How many students play video games only, no MTV?

U M G 5 How many students play video games or watch MTV (possibly both)?

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!) ==== 24

U M G U We have a symbol in math that describes this joining of regions. It is called union and looks like the letter U. So M G is the union of sets M and G. U Think U for Union!

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

U M G 5 How many students neither play video games nor watch MTV ?

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

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!

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 M G, which is read, “M intersect G” or “the intersection of M and G.”

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? 12 Almost! Let’s take another look…

GO BACK U M G 5 The whole class has 30 students, so how many are not represented in the diagram so far? #(U) = 30,U #(M) = 17M #(G) = 12.G #(M G) = 5

Almost! Let’s take another look… GO BACK U M G 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 S trawberry S hortcake GO BACK

Remember… U = the set of all students in the classset M = the set of students who watch MTVset G = the set of students who watch MTVset 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 website 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 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.