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Everything in the solar system is gravitationally bound by the Sun. | ∀x (In(x, solarSystem) → BoundBy(x, sun, gravitationally)) |
No planets gravitationally bound by the Sun are rogue planets. | ∀x (Planet(x) ∧ BoundBy(x, sun, gravitationally) → ¬(Planet(x) ∧ Rogue(x))) |
All orphan planets are rogue planets. | ∀x (Planet(x) ∧ Orphan(x) → Planet(x) ∧ Rogue(x)) |
If PSO J318.5−22 is not both a rogue planet and a planet gravitationally bound by the Sun, then it is a rogue planet. | ¬(Planet(pSOJ318.5-22) ∧ Rogue(pSOJ318.5-22) ∧ BoundBy(pSOJ318.5-22, sun, gravitationally)) → (Planet(pSOJ318.5-22) ∧ Rogue(pSOJ318.5-22)) |
PSO J318.5−22 is an orphan planet. | Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22) |
PSO J318.5−22 is an orphan planet or it does not have the Sun as its star, or both. | (Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∨ ¬SunAs(pSOJ318.5-22, star) |
If PSO J318.5−22 is an orphan planet or it does not have the Sun as the star, or both, then PSO J318.5−22 neither is an orphan planet nor does it have the Sun as the star. | (Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∨ ¬SunAs(pSOJ318.5-22, star) → (¬(Planet(pSOJ318.5-22) ∧ Orphan(pSOJ318.5-22)) ∧ ¬SunAs(pSOJ318.5-22, star)) |
Sam is doing a project. | ∃x (Project(x) ∧ Do(sam, x)) |
A project is written either in C++ or Python. | ∀x (Project(x) → (WrittenIn(x, cplusplus) ⊕ WrittenIn(x, python))) |
If Sam does a project written in Python, he will not use a Mac. | ∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac)) |
Sam is using a Mac. | Use(sam, mac) |
If Sam uses a Mac, he will play a song. | ∃x (Use(sam, mac) ∧ Song(x) → Play(sam, x)) |
If a song is not titled "Perfect," Sam will never play it. | ∀x (Song(x) ∧ Play(sam, x) → Titled(x, perfect)) |
The project Sam is doing is written in C++. | ∀x (Project(x) ∧ Do(sam, x) ∧ WrittenIn(x, cplusplus)) |
The song Sam is playing is titled "Perfect". | ∀x (Song(x) ∧ Play(sam, x) ∧ Titled(x, perfect)) |
If a song is titled "Perfect", Sam will play it. | ∀x (Titled(x, perfect) → Play(sam, x)) |
All rabbits have fur | ∀x (Rabbit(x) → Have(x, fur)) |
Some pets are rabbits. | ∃x (Pet(x) ∧ Rabbit(x)) |
Some pets do not have fur. | ∃x ∃y (Pet(x) ∧ Pet(y) ∧ ¬Have(x, fur) ∧ ¬Have(y, fur)) |
All social media applications containing chat features are software. | ∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, chatFeature) → Software(x)) |
All social media applications that allow users to send messages to each other have chat features. | ∀x (SocialMedia(x) ∧ Application(x) ∧ AllowToSendTo(x, user, message) → Contain(x, chatFeature)) |
All social media applications have chat features or video features. | ∀x (SocialMedia(x) ∧ Application(x) → Contain(x, chatFeature) ∨ Contain(x, videoFeature)) |
All social media applications that have video features allow users to upload videos. | ∀x (SocialMedia(x) ∧ Application(x) ∧ Contain(x, videoFeature) → Allow(x, user, uploadVideo)) |
All software that is social media applications are computer programs. | ∀x (SocialMedia(x) ∧ Application(x) ∧ Software(x) → ComputerProgram(x)) |
All social media applications that have high engagement metrics are addictive. | ∀x (SocialMedia(x) ∧ Application(x) ∧Have(x, highEngagementMetric) → Addictive(x)) |
If a social media application is addictive, then it is not ideal for preteens. | ∀x (SocialMedia(x) ∧ Application(x) ∧ Addictive(x) → ¬IdealFor(x, preteen)) |
TikTok is a social media application, and it is not ideal for preteens. | SocialMedia(tikTok) ∧ Application(tikTok) ∧ ¬IdealFor(tikTok, preteen) |
TikTok is a computer program. | ComputerProgram(tikTok) |
TikTok is either ideal for preteens or a computer program. | IdealFor(tikTok, preteen) ⊕ ComputerProgram(tikTok) |
TikTok is does not have chat features or it is not a computer program. | ¬Contain(tikTok, chatFeature) ∨ ¬ComputerProgram(tikTok)) |
TikTok either has chat features or is a computer program. | Contain(tikTok, chatFeature) ⊕ ComputerProgram(tikTok)) |
Ordinary is an unincorporated community. | UnincorporatedCommunity(ordinary) |
Located within Elliot County, Ordinary is on Kentucky Route 32. | LocatedIn(ordinary, elliotCounty) ∧ On(ordinary, kentuckyRoute32) |
Ordinary is located northwest of Sandy Hook. | LocatedNorthwestOf(ordinary, sandyHook) |
There are no unincorporated communities along Kentucky Route 32. | ∀x (On(x, kentuckyRoute32) → ¬UnincorporatedCommunity(x)) |
There is an unincorporated community located in Elliot County. | ∃x (UnincorporatedCommunity(x) ∧ LocatedIn(x, elliotCounty)) |
All young adults at the event like independence. | ∀x (At(x, event) ∧ YoungAdult(x) → Like(x, independence)) |
All college students at the event are young adults. | ∀x (At(x, event) ∧ CollegeStudent(x) → YoungAdult(x)) |
All Yale students at the event are college students. | ∀x (At(x, event) ∧ YaleStudent(x) → CollegeStudent(x)) |
Everyone at the event is a Yale student or a Harvard student. | ∀x (At(x, event) → (YaleStudent(x) ⊕ HarvardStudent(x))) |
All Harvard students at the event are diligent. | ∀x (At(x, event) ∧ HarvardStudent(x) → Diligent(x)) |
Susan is at the event, and if Susan is a Harvard student, then she is a young adult. | At(susan, event) ∧ (HarvardStudent(susan) → YoungAdult(susan)) |
If Susan is a Yale student, then she does not like independence. | YaleStudent(susan) → ¬Like(susan, independence) |
Susan is a college student. | CollegeStudent(susan) |
Susan likes independence and is diligent. | Like(susan, independence) ∧ Diligent(susan) |
Susan is not both diligent and likes independence. | ¬(Like(susan, independence) ∧ Diligent(susan)) |
Vic DiCara plays guitar and bass. | Play(vicDicara, guitar) ∧ Play(vicDicara, bass) |
The only style of music Vic DiCara plays is punk music. | ∀x (Music(vicDicara, x) → ¬(x=punk))) |
Vic DiCara played in the band Inside Out. | Band(vicDicara, insideOut) |
Inside Out was a punk band. | Music(insideOut, punk) |
A musician from Inside Out plays bass. | ∃x (Band(x, insideOut) ∧ Play(x, bass)) |
All professional athletes spend most of their time on sports. | ∀x (ProfessionalAthlete(x) → SpendOn(x, mostOfTheirTime, sports)) |
All Olympic gold medal winners are professional athletes. | ∀x (OlympicGoldMedalWinner(x) → ProfessionalAthlete(x)) |
No full-time scientists spend the majority of their time on sports. | ∀x (FullTimeScientist(x) → ¬SpendOn(x, mostOfTheirTime, sports)) |
All Nobel physics laureates are full-time scientists. | ∀x (NobelPhysicsLaureate(x) → FullTimeScientist(x)) |
Amy spends the most time on sports, or Amy is an Olympic gold medal winner. | SpendOn(amy, mostOfTheirTime, sports) ∨ OlympicGoldMedalWinner(amy) |
If Amy is not a Nobel physics laureate, then Amy is not an Olympic gold medal winner. | ¬NobelPhysicsLaureate(amy) → ¬OlympicGoldMedalWinner(amy) |
Amy is a professional athlete. | ProfessionalAthlete(amy) |
Amy is neither a full-time scientist nor an Olympic gold medal winner. | ¬(FullTimeScientist(amy) ∨ OlympicGoldMedalWinner(amy)) |
If Amy is not an Olympic gold medal winner, then Amy is a Nobel physics laureate. | ¬OlympicGoldMedalWinner(amy) → NobelPhysicsLaureate(amy) |
All red fruits that grow in Ben's yard contain some Vitamin C. | ∀x ((GrownIn(x, benSYard) ∧ RedFruit(x)) → Contain(x, vitaminC)) |
All apples that grow in Ben's yard are red fruits. | ∀x (GrownIn(x, benSYard) ∧ Is(x, apple) → RedFruit(x)) |
All fruits that grow in Ben's yard and contain some Vitamin C are healthy. | ∀x ((GrownIn(x, benSYard) ∧ Contain(x, vitaminC)) → healthy(x)) |
No fruits that grow in Ben's yard and are healthy are on a warning list. | ∀x ((GrownIn(x, benSYard) ∧ Healthy(x)) → ¬On(x, warningList)) |
The cherries grow in Ben's yard. | GrownIn(cherry, benSYard) |
If cherries are not apples and are not healthy, then they are red fruits. | ¬(Healthy(cherry) ∧ Is(cherry, apple)) → RedFruit(cherry) |
The cherries are apples. | Is(cherry, apple) |
The cherries either contain some amount of vitamin C or are on a warning list. | Contain(cherry, vitaminC) ⊕ On(cherry, warningList) |
The cherries are either on a warning list or are red. | On(cherry, warningList) ⊕ RedFruit(cherry) |
If the cherries are either healthy or are on a warning list, then they are not red. | BeneficialTo(cherry, people) ⊕ On(cherry, warningList))) → ¬RedFruit(cherry) |
If the cherries are either on a warning list or are red, then they are not healthy and do not contain any amount of vitamin C. | On(cherry, warningList) ⊕ RedFruit(cherry)) → ¬(BeneficialTo(cherry, people) ∧ Contain(cherry, vitaminC) |
Everyone working at Meta has a high income. | ∀x (WorkAt(x, meta) → HighIncome(x)) |
A person with a high income will not take a bus to their destination. | ∀x (HighIncome(x) → ¬MeansToDestination(x, bus)) |
People will either take a bus or drive to their destination. | ∀x (MeansToDestination(x, bus) ⊕ MeansToDestination(x, drive)) |
Everyone who has a car will choose to drive to their destination. | ∀x (HaveCar(x) → MeansToDestination(x, drive)) |
No students drive to their destination. | ∀x (Student(x) → ¬ MeansToDestination(x, drive)) |
James has a car or works at Meta. | HaveCar(james) ∨ WorkAt(james, meta) |
James has a high income. | HighIncome(james) |
James does not have a high income. | ¬HighIncome(james) |
James is a student. | Student(james) |
James drives to his destination or he is a student. | MeansToDestination(x, drive) ∨ Student(james) |
James either drives to their destination or is a student. | MeansToDestination(x, drive) ⊕ Student(james) |
If James either drives to his destination or is a student, then he has a high income and is a student. | (MeansToDestination(x, drive) ⊕ Student(james)) → (HighIncome(james) ∧ Student(james)) |
Everyone at the business conference is either an investor or an entrepreneur. | ∀x (At(x, businessConference) → (Investor(x) ⊕ Entrepreneur(x))) |
None of those at the business conference who enjoy the opportunity of starting a business prefer a planned economy. | ∀x ((At(x, businessConference) ∧ Enjoy(x, opportunityOfStartingOwnBusiness)) → ¬Prefer(x, plannedEconomy)) |
All entrepreneurs at the business conference enjoy the opportunity of starting a business. | ∀x ((At(x, businessConference) ∧ Entrepreneur(x)) → Enjoy(x, opportunityOfStartingOwnBusiness)) |
Everyone at the business conference who enjoys state ownership of means of production prefers a planned economy. | ∀x ((At(x, businessConference) ∧ Enjoy(x, stateOwnershipOfMeansOfProduction)) → Prefer(x, plannedEconomy)) |
Everyone at the business conference who is an ardent communist prefers state ownership of the means of production. | ∀x ((At(x, businessConference) ∧ ArdentCommunist(x)) → Prefer(x, stateOwnershipOfMeansOfProduction)) |
Ho is at the business conference and prefers state ownership of the means of production. | At(ho, businessConference) ∧ Prefer(ho, stateOwnershipOfMeansOfProduction) |
Ho is not an ardent communist. | ¬ArdentCommunist(ho) |
Ho is an investor or is not an ardent communist. | Investor(ho) ∨ (¬ArdentCommunist(ho)) |
No television stars are certified public accountants. | ∀x (TelevisionStar(x) → ¬CertifiedPublicAccoutant(x)) |
All certified public accountants have good business sense. | ∀x (CertifiedPublicAccoutant(x) → Have(x, goodBusinessSense)) |
All television stars have good business sense. | ∀x (TelevisionStar(x) → Have(x, goodBusinessSense)) |
Some students in the class who are good at math are also good at chemistry. | ∃x ∃y (StudentInTheClass(x) ∧ GoodAt(x, math) ∧ GoodAt(x, chemistry) ∧ (¬(x=y)) ∧ StudentInTheClass(y) ∧ GoodAt(y, math) ∧ GoodAt(y, chemistry)) |
All students in the class who are good at chemistry enjoy conducting experiments. | ∀x ((StudentInTheClass(x) ∧ GoodAt(x, chemistry)) → Enjoy(x, conductingExperiment)) |
All students in the class that enjoy conducting experiments are good at planning. | ∀x ((StudentInTheClass(x) ∧ Enjoy(x, conductingExperiment)) → GoodAt(x, planning)) |
None of the students who are good at planning failed the class. | ∀x ((StudentInTheClass(x) ∧ GoodAt(x, planning)) → ¬Failed(x, theClass)) |
James is a student in the class; he is either good at chemistry and failed the class, or bad at chemistry and passed the class. | StudentInTheClass(james) ∧ (¬(GoodAt(james, chemistry) ⊕ Failed(james, theClass))) |
James is good at planning. | GoodAt(james, planning) |