## Document Preview:

Name Tutor Date Subject Set Theory Mathematically the term set points out to an object belonging to its specified state (Jech p 1). George Cantor and his counterpart Richard Dedekind came up with the set theory which made the conceptualization of this mathematical term more evident during the 1870s. However more researchers have come up with distinct methodologies on sets which have enabled the contemporary mathematical society to understand the relationship existing in the wide range of structures for real number lines as well as the study of consistency of transfinite cardinal numbers. Apparently the game theory also borrows significant concepts relevant to the set theory. Take for example the card game Taboo. The game is rather of either team understands the elements that make a set he or she will highly likely make out the intended word of the set. Also if by chance there are elements which intercede each other in the set then the player would easily relate to the anticipated word of the set hence helping their team to earn more points. Work Cited Halmos Paul R. Naive Set Theory. 2017. Print. Jech Thomas J. Set Theory. Berlin: Springer 1997. Internet resource. Shen Alexander and Nikolai K. Vereshchagin. Basic Set Theory. Providence R.I: American Mathematical Society 2002. Print. Tinsman Brian. Game Inventor's Guidebook: How to Invent and Sell Board Games Card Games Role-Player Games and Everything in Between!F+W Media 2011. Internet resource. Index [...]

## Order Description:

Task Task 4, Module 4 – How are sets utilized within the game? When you consider “sets” as a collection of objects or information, it turns out that most games have some type of set elements (some more than others)! How does your game utilize sets? Specifically: • What sets are present in your game? • What are the elements of those sets? • Are there elements in the unions and intersections of these sets? • Can an understanding of these sets help a player develop a winning strategy? Lesson Pre-Lesson 1. Investigate Basic Set Operations Work through the Khan Academy tutorials on sets www.khanacademy.org 2. Investigate Venn Diagrams and Sets Click on the Venn Diagram and investigate set further: www.mathsisfun.com 3. Investigate Set Notation www.mathsisfun.com Taboo! Have you ever played the card game Taboo? It’s an interesting party game with fairly simply rules: the players are broken up into two teams that take turns trying to guess a mystery word. On a team’s turn one member has to sit with the other team and draw a card. At the top of this card is the mystery word that her team has to figure out based on what she says, but beneath that word is a list of words that she can’t say (that are “taboo”). Once she is ready, a timer is started! For instance, if the card was {Fish| Water, Animal, Fins}, then the player is trying to make her team guess the word “fish” without saying water, animal, or fins. Maybe she can say something like “You saw a lot of them in Finding Nemo.” If the team guesses the word then they earn a point and the card holder draws a new card. If that card holder accidentally says one of the Taboo words, then the team actually loses a point. The player keeps going until the timer runs out, at which point it’s the other team’s turn to play! Sounds like so much fun right? Why don’t you play a game? If you don’t have your own set, feel free to use these below: Make sure that you don’t print them double sided though! What does Taboo have to do with math though? Taboo deals with a branch of mathematics called “set theory.” To explore this, sit down with your team and spread out all of the cards so that everyone can see and reach everything. Take a few minutes to sort the cards into whatever different groups you feel are appropriate. Once you are finished, share your groupings with the other team(s) and see what they came up with. Be prepared to defend your decisions! Common Notations and Symbols Let’s assume that we have two sets called A and B. They are like two “boxes” that contain the following things: A = {b, o, x} B = {c, o, n, t, a, i, e, r} Since these are filled with letters, let’s say that they exist in the universe of the alphabet: U = {a, b, c,…, y, z} Use these three sets as a reference while going through the chart below (click on the image to access the chart): Venn Diagram Design Sets aren’t just good for organizing objects. They are also an excellent means of representing data that have shared characteristics. Take one of the longest-running feuds of the 20th Century: Coca Cola vs. Pepsi Between these two carbonated beverage giants, which option would you choose? • Coke • Pepsi • No preference (you like them both) • Neither Now that you’ve made your choice, partner up with someone to go around and find out other people’s opinions. See if you can get around a dozen more people each, and then pool your information together. Does your data look neat and tidy just yet? Consider where all of the information falls from a visual sense because you can have three possibilities: Which scenarios does each one represent? Which one best models what you and your partner found? Once you determine this, see if you can figure out the best way to “insert” your survey findings into this Venn Diagram so that it makes sense. Once you are finished, share your Venn Diagram with other groups and see if everyone can combine their Venn Diagrams into one all-encompassing diagram. Ready to up the ante on this? What would happen if you added a third choice to the mix? Suppose we wanted to compare Coke to Pepsi AND Mountain Dew. What are all the possibilities that we could have now? Sketch these out. Once you have that done, let’s assume that you surveyed 50 more people, and of those people 21 like Pepsi, 32 like Coke, 24 like Mountain Dew, 15 like Coke and Mountain Dew, 7 like Pepsi and Mountain Dew, 13 like Pepsi and Coke, and finally 5 like all three drinks. What does this look like as a Venn Diagram? Can you correctly identify all of the parts in that diagram? If you’re stumped, try the video below as a guide: Finite Math: Venn Diagram Practice Problems by Brandon Foltz www.youtube.com Project Assignment – Task 4: How are sets utilized within the game? When you consider “sets” as a collection of objects or information, it turns out that most games have some type of set elements (some more than others)! How does your game utilize sets? Specifically: • What sets are present in your game? • What are the elements of those sets? • Are there elements in the unions and intersections of these sets? • Can an understanding of these sets help a player develop a winning strategy? Submit this into Moodle. ____________________________________________________________ Module 5/Week 5 Main Topic Logic Course Learning Outcome(s) for the Week • Apply logic and problem solving to explore mathematical sets and models Discussion Venn Diagrams are a useful tool when trying to pull together survey results. That's what we're up to this week: conduct a survey and share your results here. Once we get enough responses, we'll pull it together into a Venn Diagram and see what it looks like! Part 1 (during week 5) Here's your survey: Which pet do you prefer? • Dogs • Cats • Reptiles • Birds • No preference • None of those listed Ask your family members, friends, coworkers, strangers on the street, whatever! Just get us some data and share it with the group. Part 2 (during week 6) Based on all of the data that was shared, build a Venn Diagram that accurately models the information presented. You’re not doing this individually, but instead need to build this as a group! This may involve you coming into this discussion more times than usual to keep the conversation going.

Subject Area: Mathematics

Document Type: Paraphrasing