DM Slides - 26 July

Decision Making 1

Decision Making LessonsLesson 1: Introduction to Decision Making Lesson 13: Logical Puzzles - Conditional ScenariosLesson 2: Syllogisms I Lesson 14: Interpreting Information - IntroductionLesson 3: Syllogisms II Lesson 15: Interpreting Information - Graphs ILesson 4: Venn Diagrams I Lesson 16: Interpreting Information - Graphs IILesson 5: Venn Diagrams II Lesson 17: Interpreting Information - MapsLesson 6: Probabilistic Reasoning I Lesson 18: Interpreting Information - TextLesson 7: Probabilistic Reasoning II Lesson 19: Interpreting Information - TablesLesson 8: Logical Puzzles (Crosshatch vs Fill-In I) Lesson 20: Recognising Assumptions - TheoryLesson 9: Logical Puzzles (Crosshatch vs Fill-In II) Lesson 21: Recognising Assumptions - Examples ILesson 10: Logical Puzzles Ordered Questions Lessons 22 : Recognising Assumptions - Examples IILesson 11: Logical Puzzles - Tabular Questions Lesson 23: Tips from the ExpertsLesson 12: Logical Puzzles - Spatial Equations Lesson 24: Summary and Overview

Introduction to Decision Making Lesson 1 3

Introduction to Decision Making Introduction to Decision MakingWhat is Decision Making?• New section for 2017• Tests your ability to:11. Apply logic to reach a conclusion22. Analyse statistical information33. Evaluate arguments

Introduction to Decision Making31 MINUTES29 QUESTIONS29 SCENARIOS64 SECONDS PER QUESTION 5

Introduction to Decision MakingWhat are the different question types? • Syllogisms - When you are given two or more statements and have to use logical reasoning to decide what conclusions follow. • Venn Diagrams - You may be presented with a set of statements and set of different Venn diagrams as response options. • Probabilistic Reasoning - Select best possible response for a question relating to probability.

Introduction to Decision MakingWhat are the different question types?• Logical Puzzles - Given a series of statements and facts and need to infer information from this.• Interpreting Information - Find which conclusion best follows an argument.• Recognising Assumptions - Test your ability to evaluate how strong an argument is in support for or against a solution to a particular problem.

Syllogisms I Lesson 2 8

SyllogismsWhat are syllogisms?Syllogisms contain two or more statements which are followed by a series of conclusions. Use logical reasoning to deduce which conclusions follow from information given. The information may not make actual sense e.g. All bananas are vegetables. All vegetables are desserts.

SyllogismsKey tips for syllogism questions • Once you crack the technique for syllogisms, it becomes much easier. • Read all the information multiple times, until it makes logical sense. • Pay special attention to words such as ‘some’, ‘none’, ‘all’, and only. • Do not make assumptions about the information using external knowledge. • Draw Venn Diagrams wherever possible.

SyllogismsThe Venn Approach It is recommended that you use Venn diagrams.These are not as straightforward as the ones in mathematics exams. We will now go through the different types of Venn diagrams and when to use them.

Pure Theory of Venn Diagrams 12

SyllogismsPattern 1: Some A are BAB Some A are not B Some B are not A Some A are B Some B are A

SyllogismsExample - Some Giraffes are SharksGiraffes Sharks Some giraffes are not sharks Some sharks are not giraffes Some giraffes are sharks Some sharks are giraffes

Pattern 2: All A are B Syllogisms B All A are B Some A are B A Some B are A

SyllogismsExample: All beaches are sightsSightsBeaches All beaches are sights Some beaches are sights Some sights are beaches

SyllogismsPattern 3: Some A are not B What can be deduced? Some A are B AB

SyllogismsExample - Some snakes are not reptiles What can be deduced? Some Snakes are Reptiles SR

SyllogismsPattern 4: No A are BAB No A is B

SyllogismsExample: No spreads are peanut butterSpreads Peanut No Spreads are Peanut Butter Butter

SyllogismsPattern 5: Some A are B and some B are C ABCBetween A and B Between B and C Between A and CSome A are B Some B are C Unknown RelationshipSome B are A Some C are B

SyllogismsPattern 5: Some A are B and some B are C ABC Between A and C There could be a relationship - either there can be items that are A, B and C, or there can be items that are just A. However, we do not know this so when we answer questions we assume there is no relationship.

SyllogismsPattern 5: Some A are B and some B are C ABCExample Statements:• Some A is C Not a conclusion• All A is C Not a conclusion• No A is C Not a conclusion (there could be a relationship)

SyllogismsExample: Some buildings are skyscrapers. Some skyscrapers are towersBuildings Skyscrapers Tower Buildings & Skyscrapers Some buildings are skyscrapers Some skyscrapers are buildings Skyscrapers & Towers Some skyscrapers are towers Some towers are skyscrapers Buildings & Towers Unknown relationship

Syllogisms Between A and C All A are CPattern 6: All A are B and all B are C Some A are C Some C are A C B Between B and C All B are C Between A and B Some B are C All A are B Some C are B A Some A are B Some B are A

SyllogismsExample: All cities are countries and all countries are continentsContinents Cities & Countries Cities & ContinentsCountries All Cities are countries All cities are continents Some cities are countries Some cities are continents Cities Some countries are cities Some continents are cities Countries & Continents All countries are continents Some countries are continents Some continents are countries

Syllogisms Between A and C Some A are CPattern 7: Some A are B, and all B are C Some C are A Between A and B Between B and C All B are C A B C Some A are B Some B are C Some B are A Some C are B

SyllogismsExample: Some shoes are slippers and all slippers are footwearShoes Slippers Shoes & Slippers Some shoes are slippers Footwear Some slippers are shoes Slippers & Footwear All slippers are footwear Some slippers are footwear Some footwear are slippers Shoes & Footwear Some shoes are footwear Some footwear are shoes

SyllogismsPattern 8: All A are B, and some B are C B Between A and B Between A and CA Unknown relationship C All A are B Some A are B Between B and C Some B are C Some B are A Some C are B

SyllogismsExample: All mobiles are gadgets and some gadgets are portable Gadgets Portables Between mobiles and Between mobiles andMobiles gadgets portables All mobiles are gadgets Unknown relationship Some mobiles are gadgets Some gadgets are mobiles Between gadgets and portables Some gadgets are portables Some portables are gadgets

SyllogismsPattern 9: All B are A and all C are A What can be deduced? A C Between A and B Between A and CB All B are A All C are A Some B are A Some C are A Some A are B Some A are C Between B and C Unknown relationship

SyllogismsExample: All cars are trucks and all lorries are trucks Trucks Lorries Between trucks and Between trucks andCars cars lorries All cars are trucks All lorries are trucks Some trucks are cars Some lorries are trucks Some cars are trucks Some trucks are lorries Between cars and lorries Unknown relationship

SyllogismsPattern 10 - All A are B and no B are CAB C Between A and B Between A and C All A are B No A are C Some A are B No C are A Some B are A Some A are not C Some C are not A Between B and C No B are C No C are B Some B are not C Some C are not B

SyllogismsExample - All symphonies are trumpets and no trumpets are clarinetsSymphonies Clarinets Symphonies and Symphonies and clarinets Trumpets trumpets No symphonies are clarinets All symphonies are No clarinets are symphonies trumpets Some clarinets are not Some symphonies are symphonies trumpets Some symphonies are not Some trumpets are symphonies clarinets Trumpets and clarinets No trumpets are clarinets No clarinets are trumpets Some clarinets are not trumpets Some trumpets are not clarinets

SyllogismsPattern 11 - All A are B and no A are C Between A and C B Between A and B No A are CA No C are A Some A are not C Some C are not A C All A are B Some A are B Some B are A Between B and C Some B are not C

SyllogismsExample: All cherries are pencils and no cherries are pillowsCherries Pillows Between cherries and Between cherries and pillows pencils No cherries are pillows No pillows are cherries All cherries are pencils Some cherries are not pillows Some cherries are Some pillows are not cherries pencils Some pencils are Between pencils and cherries pillows Some pencils are not Pencils pillows

SyllogismsPattern 12 - Some A are B and no B are C Between A and C Between A and B Some A are not CCA B Some A are B Some B are A Between B and C No B are C No C are B Some B are not C Some C are not B

SyllogismsExample: Some psychology students are graduates and no graduates are mathematicians Between A and C Some psychology students are not mathematiciansPsychology Graduates Mathematicians Between psychology Between graduates and students are graduates mathematicians Some psychology No graduates and students are graduates mathematicians Some graduates are No mathematicians are psychology students graduates Some graduates are not mathematicians

SyllogismsGeneral RulesTake the approach of the question of being a riddle. Use these shortcutsNo x + No y No relationshipAll x + All y All connectedAll x + Some y No immediate conclusionSome x + All y Some relationshipSome x + No y Some are not relatedSome x + Some y No immediate conclusion

Syllogisms II Lesson 3 40

Syllogisms: Example 1 41

SyllogismsExample 1: SyllogismsSome cockroaches are crocodiles. All the crocodiles are strawberries.Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow.1. All the cockroaches are crocodiles.2. Some cockroaches are strawberries.3. Some crocodiles are strawberries4. All the cockroaches are strawberries. 42

SyllogismsExample 1: SyllogismsSome cockroaches are crocodiles. All the crocodiles Cockroaches Crocodiles Strawberriesare strawberries.1. All the cockroaches are crocodiles.2. Some cockroaches are strawberries.3. Some crocodiles are strawberries4. All the cockroaches are strawberries. Pattern 7 43

SyllogismsExample 1: Syllogisms All the cockroaches are crocodiles. FALSESome cockroaches are crocodiles. All the crocodilesare strawberries. Cockroaches Crocodiles Strawberries1. All the cockroaches are crocodiles.2. Some cockroaches are strawberries.3. Some crocodiles are strawberries4. All the cockroaches are strawberries. 44

SyllogismsExample 1: SyllogismsSome cockroaches are crocodiles. All the crocodiles Some cockroaches are strawberriesare strawberries. TRUE1. All the cockroaches are crocodiles. Cockroaches Crocodiles Strawberries2. Some cockroaches are strawberries.3. Some crocodiles are strawberries4. All the cockroaches are strawberries. 45

SyllogismsExample 1: Syllogisms Some crocodiles are strawberries TRUESome cockroaches are crocodiles. All the crocodilesare strawberries. Cockroaches Crocodiles Strawberries1. All the cockroaches are crocodiles.2. Some cockroaches are strawberries.3. Some crocodiles are strawberries4. All the cockroaches are strawberries. 46

SyllogismsExample 2: Syllogisms All the cockroaches are strawberries FALSESome cockroaches are crocodiles. All the crocodilesare strawberries. Cockroaches Crocodiles Strawberries1. All the cockroaches are crocodiles.2. Some cockroaches are strawberries.3. Some crocodiles are strawberries4. All the cockroaches are strawberries. 47

Syllogisms: Example 2 48

SyllogismsExample 2: SyllogismsA group of friends at Cambridge university are fromeither London or Manchester. They study eitherGeography or Economics. Some of the students arefrom London and the rest study EconomicsPlace ‘Yes’ if the conclusion does followPlace ‘No’ if the conclusion does not followAll of the Economic students are from Manchester. 49

SyllogismsExample 2: SyllogismsA group of friends at Cambridge university are from either London or Manchester. They studyeither Geography or Economics. Some of the students are from London and the rest studyEconomicsAll the students from London Remaining students“Some of the students are from London” “The rest study Economics”• Study either subject • Study Economics• Live in London • Live in Manchester 50