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All people in this midwest town with a lot of disposable income have a horse ranch.
∀x (InThisMidwestTown(x) ∧ Have(x, disposableIncome) → Have(x, horseRank))
If people in this midwest town compete in horse dressage shows, then they have a lot of disposable income.
∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → Have(x, disposableIncome))
If people in this midwest town compete in horse dressage shows, then they have invested in high-quality equestrian gear and equipment.
∀x (InThisMidwestTown(x) ∧ CompeteIn(x, horseDressageShow) → InvestedIn(x, equestrianGearAndEquipment))
If people in this midwest town regularly ride horses for pleasure and sport, then they do not live in cramped residential buildings.
∀x (InThisMidwestTown(x) ∧ RegularlyRideHorseForPleasure(x) → ¬LiveIn(x, crampedBuilding))
Manny is in this midwest town, and she either has a horse ranch and lives in a cramped residential building, or she does neither.
InThisMidwestTown(manny) ∧ ¬(Have(manny, horseRanch) ⊕ LiveIn(manny, crampedBuilding))
Manny regularly rides horses for pleasure and sport.
RegularlyRideHorsesForPleasure(manny)
Manny competes in horse dressage shows and has invested in high-quality equestrian equipment and gear.
CompeteIn(manny, horseDressageShow) ∧ InvestedIn(manny, equestrianGearAndEquipment)
If Manny either has a horse ranch or competes in horse dressage shows, then Manny has not invested in high-quality equestrian equipment and gear.
¬(HaveAHorseRanch(manny) ⊕ CompeteIn(manny, horseDressageShow)) → ¬InvestedIn(manny, equestrianGearAndEquipment)
A roundel is a rounded artillery fortification.
∀x (Roundel(x) → (Rounded(x) ∧ ArtilleryFortification(x)))
A roundel is not higher than adjacent walls.
∀x ∀y ((Roundel(x) ∧ AdjacentWalls(x,y)) → ¬Higher(x, y))
Cannons can be deployed on artillery fortifications.
∀x (ArtilleryFortification(x) → DeployCannons(x))
Roundels are the oldest artillery fortifications.
∀x ∀y ((Roundel(x) ∧ ArtilleryFortification(y)) → Older(x, y))
Battery towers are artillery fortifications.
∀x (BatteryTower(x) → ArtilleryFortification(x))
Cannons can be deployed on battery towers.
∀x (BatteryTower(x) → DeployCannons(x))
Roundels are older than battery towers.
∀x ∀y ((Roundel(x) ∧ BatteryTower(y)) → Older(x, y))
Battery towers are higher than adjacent walls.
∀x ∀y ((BatteryTower(x) ∧ AdjacentWall(x,y)) → Higher(x, y))
Cannons can be deployed on roundels.
∀x (Roundel(x) → DeployCannons(x))
Tissues are soft.
∀x (Tissue(x) → Soft(x))
Some papers are tissues.
∃x ∃y (Paper(x) ∧ Paper(x) ∧ Tissue(x) ∧ Tissue(y) ∧ ¬(x=y))
Some papers are hard.
∃x ∃y (Paper(x) ∧ Paper(y) ∧ Hard(x) ∧ Hard(y) ∧ ¬(x=y))
All volunteers receive intangible benefits for their work.
∀x (Volunteer(x) → Receive(x, intangibleBenefit))
Volunteers work regularly or on an as-needed basis.
∀x (Volunteer(x) → WorkRegularly(x) ⊕ WorkAsNeeded(x))
Some volunteers are trained.
∃x (Volunteer(x) → Trained(x))
Volunteers work in groups or individually.
∀x (Volunteer(x) → (WorkInGroup(x) ∨ WorkIndividually(x)))
Environmental volunteers contribute toward environmental management or conservation.
∀x (Volunteer(x) ∧ Environmental(x) → (ContributeTo(x, environmentalManagement) ∨ ContributeTo(x, environmentalConservation)))
Participating in natural disaster response is an example of volunteers working in groups on an as-needed basis.
∃x (Volunteer(x) ∧ ContributeTo(x, naturalDisasterResponse) → WorkInGroup(x) ∧ WorkAsNeeded(x))
Volunteers who participate in natural disaster response receive intangible benefits for their work.
∀x (Volunteer(x) ∧ ContributeTo(x, naturalDisasterResponse) → Receive(x, intangibleBenefit))
Environmental volunteers work in groups.
∀x (Volunteer(x) ∧ Environmental(x) → WorkInGroup(x))
To be a volunteer, you must be trained.
∀x (Volunteer(x) → Trained(x))
All people in this tech company who are consistent and enjoy sticking to their regular routines do not like surprises.
∀x (InThisTechCompany(x) ∧ Consistent(x) ∧ StickTo(x, theirRegularRoutine) → ¬Like(x, surprise))
People in this tech company who wear the same flannel shirts every day are consistent and enjoy sticking to their regular routines.
∀x (InThisTechCompany(x) ∧ ∃y (flannelShirt(y) ∧ WearEveryday(x, y)) → Consistent(x) ∧ StickTo(x, theirRegularRoutine))
People in this tech company who do not like shopping for clothes wear the same flannel shirts every day.
∀x (InThisTechCompany(x) ∧ ¬LikeShoppingFor(x, clothes) → ∃y (flannelShirt(y) ∧ WearEveryday(x, y)))
Old people living in stable homes do not like surprises.
∀x (InThisTechCompany(x) ∧ Old(x) ∧ LiveIn(x, stableHome) → ¬Like(x, surprise))
People in this tech company who have very high energy and are impulsive like surprises.
∀x (InThisTechCompany(x) ∧ Have(x, highEnergy) ∧ Impulsive(x) → ¬Like(x, surprise))
Mike works in this tech company.
InThisTechCompany(mike)
If Mike is not a person who wears the same flannel shirts every day, has very high energy, and is impulsive, then Mike either is very consistent and enjoys sticking to his regular routines or does not like surprises.
¬(∃y (flannelShirt(y) ∧ WearEveryday(x, y)) ∧ Have(mike, highEnergy) ∧ Impulsive(mike)) → (Consistent(mike) ∧ StickTo(mike, theirRegularRoutine)) ⊕ ¬Like(mike, surprise)
Mike is an old person living in a stable home.
Old(mike) ∧ LiveIn(mike, stableHome)
If Mike wears the same flannel shirts every day or does not like shopping for clothes, then Mike is neither an old person living in a stable home nor does he like shopping for clothes.
(∃y (flannelShirt(y) ∧ WearEveryday(mike, y)) ∨ ¬LikeShoppingFor(mike, clothes)) → ¬(Old(mike) ∧ LiveIn(mike, stableHome)) ∧ ¬LikeShoppingFor(mike, clothes)
If Mike is not an old person living in a stable home and does not like shopping for clothes, then Mike does not like shopping for clothes.
¬(Old(mike) ∧ LiveIn(mike, stableHome)) ∧ ¬LikeShoppingFor(mike, clothes)) → ¬LikeShoppingFor(mike, clothes)
Adam owns cars.
∃x∃y (Car(x) ∧ Car(y) ∧ (x≠y) ∧ Owns(adam, x))
Adam has a favorite car.
∃x (Car(x) ∧ Favorite(adam, x))
Among the cars he owns, Adam's favorite car is European.
∀x ((Car(x) ∧ Owns(adam, x) ∧ Favorite(adam, x)) → European(x))
Adam broke his favorite car.
∀x ((Car(x) ∧ Owns(adam, x) ∧ Favorite(adam, x)) → Broke(adam, x))
Adam owns a Japanese car.
∃x (Japanese(x) ∧ Owns(adam, x))
Adam broke a European car.
∃x (European(x) ∧ Broke(adam, x))
There are no buildings in New Haven higher than 400 meters.
∀x ((Buildings(x) ∧ In(x, newHaven)) → ¬HigherThan(x, num400))
All buildings managed by Yale Housing are in New Haven.
∀x ((Buildings(x) ∧ ManagedBy(x, yaleHousing)) → In(x, newHaven))
All Manhattan skyscrapers are higher than 400 meters.
∀x ((Buildings(x) ∧ Skyscraper(x) ∧ In(x, manhattan)) → HigherThan(x, num400))
All buildings owned by Bloomberg are in Manhattan.
∀x ((Buildings(x) ∧ OwnedBy(x, bloomberg)) → Skyscraper(x) ∧ In(x, manhattan))
All buildings with the Bloomberg logo are buildings owned by Bloomberg.
∀x ((Buildings(x) ∧ HasLogo(x, bloomberg)) → OwnedBy(x, bloomberg))
Tower A is neither a building in New Haven nor a skyscraper in Manhattan.
Buildings(towerA) ∧ (¬InNewHaven(towerA)) ∧ (¬ManhattanSkyscraper(towerA))
Tower B is a skyscraper building in Manhattan with a Bloomberg logo.
Buildings(towerB) ∧ HasLogo(towerB, bloomberg) ∧ Skyscraper(towerB) ∧ In(towerB, manhattan)
Tower A is higher than 400 meters.
HigherThan(towerA, num400)
Tower A is not higher than 400 meters.
¬HigherThan(towerA, num400)
Tower A is a building with the Bloomberg logo or it is managed by Yale Housing.
HasLogo(towerB, bloomberg) ∨ ManagedBy(x, yaleHousing)
Tower A is neither a building with the Bloomberg logo nor managed by Yale Housing.
¬HasLogo(towerB, bloomberg) ∧ (¬ManagedBy(x, yaleHousing))
No fish are birds.
∀x (Fish(x) → ¬Bird(x))
An osprey is a bird.
∀x (Osprey(x) → Bird(x))
A carp is a fish.
∀x (Carp(x) → Fish(x))
All goldfish are carp.
∀x (Goldfish(x) → Carp(x))
If Bubbles is either an osprey or a goldfish, then Bubbles is not also a fish.
Osprey(bubbles) ⊕ Goldfish(bubbles) → ¬Fish(bubbles)
Bubbles is an Osprey.
Osprey(bubbles)
Bubbles is a goldfish.
Goldfish(bubbles)
Bubbles is not a goldfish.
¬Goldfish(bubbles)
Mr. and Mrs. Smith make a travel plan: they want to go to a city in California or Florida where neither of them has ever been.
∀x (WantToGoTo(mr.AndMrs.Smith, x) ∧ City(x) → (California(x) ∨ Florida(x)) ∧ NeverGo(x))
The cities in California that they are interested in are San Francisco, Los Angeles, and San Diego.
City(sanFrancisco) ∧ California(sanFrancisco) ∧ WantToGoTo(mr.AndMrs.Smith, sanFrancisco) ∧ City(losAngeles) ∧ California(losAngeles) ∧ WantToGoTo(mr.AndMrs.Smith, losAngeles) ∧ City(sanDiego) ∧ California(sanDiego) ∧ WantToGoTo(mr.AndMrs.Smith, sanDiego)
Cities in Florida that they are interested in are Orlando and Miami.
City(orlando) ∧ Florida(orlando) ∧ WantToGo(mr.AndMrs.Smith, orlando) ∧ City(miami) ∧ Florida(miami) ∧ WantToGo(mr.AndMrs.Smith, miami)
Mr. Smith has been to two cities in California.
∃x ∃y ∀z (¬(x=z) ∧ ¬(y=z) ∧ ¬(x=y) ∧ City(x) ∧ City(y) ∧ City(z) ∧ California(x) ∧ California(y) ∧ California(z) → Visit(mr.smith, x) ∧ Visit(mr.smith, y) ∧ ¬Visit(mr.smith, z))
Mrs. Smith has been to one city in Florida.
∃x ∀y (¬(x=y) ∧ City(x) ∧ City(y) ∧ Florida(x) ∧ Florida(y) → Visit(mrs.smith, x) ∧ ¬Visit(mrs.smith, y))
Mr. Smith has been to San Francisco.
∃x (City(x) ∧ Visit(mr.smith, sanFrancisco))
They have at leat one candidate city in Florida to visit.
∃x (WantToGoTo(x) ∧ City(x) ∧ Florida(x))
They have at least two candidate cities in California to visit.
∃x ∃y (¬(x=y) ∧ City(x) ∧ City(y) ∧ WantToGoTo(mr.AndMrs.Smith, x) ∧ California(x) ∧ WantToGoTo(mr.AndMrs.Smith, y) ∧ California(y))
Everything in Size Town is big or small.
∀x (In(x, sizeTown) → (Big(x) ∨ Small(x)))
All big things in Size Town are heavy.
∀x (Big(x) ∧ In(x, sizeTown) → Heavy(x))
All small things in Size Town are light.
∀x (Small(x) ∧ In(x, sizeTown) → Light(x))
All heavy things in Size Town are still.
∀x (Heavy(x) ∧ In(x, sizeTown) → Still(x))
All light things in Size Town are unstable.
∀x (Light(x) ∧ In(x, sizeTown) → Unstable(x))
All unstable things in Size Town are changing.
∀x (Unstable(x) ∧ In(x, sizeTown) → Changing(x))
All unstable things in Size Town are unpredictable.
∀x (Unstable(x) ∧ In(x, sizeTown) → Unpredictable(x))
The bird is in Size Town and it is not both heavy and still.
In(bird, sizeTown) ∧ ¬(Heavy(bird) ∧ Still(bird))
The bird is still.
Still(bird)
The bird is not still.
¬Still(bird)
The bird is unpredictable and changing.
Unpredictable(bird) ∧ Changing(bird)
The bird is unpredictable or changing.
Unpredictable(bird) ∨ Changing(bird)
The bird is either unpredictable or changing.
Unpredictable(bird) ⊕ Changing(bird)
If the bird is small or still, then it is either unpredictable or changing.
Small(bird) ∨ Still(bird) → Unpredictable(bird) ⊕ Changing(bird)
DI Ray is a police procedural television series.
TelevisionSeries(dIRay) ∧ PoliceProcedural(dIRay)
DI Ray was created and written by Maya Sondhi.
Creates(maya, dIRay) ∧ Writes(maya, dIRay)
DI Ray was produced by Jed Mercurio.
Produces(jed, dIRay)
Maya Sondhi and Jed Mercurio are both British.
British(maya) ∧ British(jed)
DI Ray was created by a Brit.
∃x (British(x) ∧ Creates(x, dIRay))
Some Brit produced a television series.
∃x ∃y(British(x) ∧ TelevisionSeries(y) ∧ Produces(x, y))
Everyone who took the bar exam can read.
∀x (Take(x, barExam) → CanRead(x))
All lawyers took the bar exam.
∀x (Lawyer(x) → Take(x, barExam))
Everyone who took the bar exam is knowledgeable about criminal procedures.
∀x (Take(x, barExam) → KnowledgeableAbout(x, criminalProceeder))
All people who got a score of 180 on the LSAT can read.
∀x (GetOn(x, scoreOf180, lSAT) → CanRead(x))
No elephants can read.
∀x (Elephant(x) → ¬CanRead(x))
If Mike can not read or is not an elephant, then Mike either took the bar exam or can read.
¬(CanRead(mike) ∧ Elephant(mike)) → Take(mike, barExam) ⊕ CanRead(mike)
Mike got 180 on the LSAT.
GetOn(mike, 180, lSAT)
Mike did not take the bar exam and is not both knowledgeable about criminal procedures and someone who got 180 on the LSAT.
¬Take(mike, barExam) ∧ ¬(KnowledgeableAbout(mike, criminalProcedures)∧ GetOn(mike, 180, lSAT))