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If a disease is mild, then no lab tests or imaging is required.
|
∀x (Disease(x) ∧ Mild(x) → ¬(RequiredFor(labTest, x) ∨ RequiredFor(imaging, x)))
|
All blood cancers are rare diseases.
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∀x (BloodCancer(x) → RareDiseases(x))
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All types of leukemia are diseases and blood cancers.
|
∀x (Disease(x) ∧ Leukemia(x) → BloodCancer(x))
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Bladder cancer is a disease and is blood cancer or Leukemia.
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Disease(bladderCancer) ∧ (BloodCancer(bladderCancer) ∨ Leukemia(bladderCancer))
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Bladder cancer is a mild disease.
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Mild(bladderCancer)
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Bladder cancer is Leukemia.
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Leukemia(bladderCancer)
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Bladder cancer is either a rare disease or a mild disease.
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RareDisease(bladderCancer) ⊕ Mild(bladderCancer)
|
There are no elements with atomic number between 61-63 that are not scarce in China.
|
∀x ((Element(x) ∧ ∃y(Between(y, num61, num63) ∧ AtomicNumber(x, y))) → ScarceIn(x, china))
|
Non-rare earth elements are not scarce in China.
|
∀x (¬RareEarthElement(x) → ¬ScarceIn(x, china))
|
All elements are either non-rare earth elements or rare earth elements.
|
∀x (¬RareEarthElement(x) ⊕ RareEarthElement(x))
|
All rare earth elements can be used for industry.
|
∀x (RareEarthElement(x) → UsedIn(x, industry))
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All rare earth elements are essential for exploring future directions of electronics.
|
∀x (RareEarthElement(x) → EssentialFor(x, electronics))
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Lithium is either a non-rare earth element and essential for exploring future directions of electronics, or is not a non-rare earth element and is not essential for exploring future directions of electronics.
|
¬(¬RareEarthElement(lithium) ⊕ EssentialFor(lithium, electronics))
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Lithium is a rare earth element.
|
RareEarthElement(lithium)
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Lithium is an element with atomic number between 61-63 and is used for batteries.
|
Element(x) ∧ ∃y(Between(y, num61, num63) ∧ AtomicNumber(x, y)) ∧ UsedFor(lithium, batteries)
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If Lithium is not essential for exploring future directions of electronics or an element with atomic number between 61-63, then Lithium is not a non-rare earth element or usable in industry.
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¬(EssentialFor(lithium, electronics) ⊕ (∃y(Between(y, num61, num63) ∧ AtomicNumber(lithium, y)))) → ¬(¬RareEarthMetals(lithium) ∨ UsedIn(lithium, industry))
|
If people don't often clean their homes, then they do not have tidy houses.
|
∀x (¬CleanOften(x, home) → ¬Have(x, tidyHouse))
|
If people don't prioritize cleaning, then they do not often clean their homes.
|
∀x (¬Prioritize(x, cleaning) → ¬CleanOften(x, home))
|
If people hire a maid or cleaning service, then they have tidy houses.
|
∀x (Hire(x, maid) ∨ Hire(x, cleaningService) → Have(x, tidyHouse))
|
If people don't care about cleanliness, then they do not prioritize cleaning.
|
∀x (¬CareAbout(x, cleanliness) → ¬Prioritize(x, cleaning))
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Either Jack does hire a maid or cleaning service and does not often clean his home, or he does not hire a maid or cleaning service nor often clean his home.
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¬(Hire(x, maid) ∨ Hire(x, cleaningService)) ⊕ ¬CleanOften(jack, home))
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Jack doesn't care about cleanliness.
|
¬(CareAbout(jack, cleanliness))
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Jack does care about cleanliness.
|
CareAbout(jack, cleanliness)
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Jack has a tidy house.
|
Have(jack, tidyHouse)
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Jack neither lives in the suburbs nor is too busy to clean.
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¬(¬CareAbout(jack, cleanliness) ∨ ¬CleanOften(jack, home)
|
Jack is overburdened and lives in the suburbs.
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¬Prioritize(jack, cleaning) ∨ ¬CareAbout(jack, cleanliness)
|
The bottle not falling is either standing upright or toppled over.
|
¬Falling(bottle) → (Upright(bottle) ⊕ ToppledOver(bottle))
|
The bottle not falling is not standing upright.
|
¬Falling(bottle) → ¬Upright(bottle)
|
The bottle not falling is toppled over.
|
¬Falling(bottle) → ToppleOver(bottle)
|
Everyone who chooses what they want to do with their time has flexible schedules.
|
∀x (ChooseWhatToDoWith(x, time) → FlexibleSchedule(x))
|
Everyone with a lot of free time chooses what they want to do with their time.
|
∀x (Have(x, lotsOfFreetime) → ChooseWhatToDoWith(x, time))
|
People either have a lot of free time or they invest in a career in which they are willing to spend the rest of their lives.
|
∀x (Have(x, lotsOfFreetime) ⊕ (∃y (InvestIn(x, y) ∧ Career(y) ∧ WillingToSpendIn(restOfLife, y))))
|
If people invest in a career in which they are willing to spend the rest of their lives, then they are hardworking individuals with high ambitions and goals for the future.
|
∀x (∃y (InvestIn(x, y) ∧ Career(y) ∧ WillingToSpendIn(restOfLife, y)) → Hardworking(x))
|
If people are hardworking individuals with high ambitions and goals for the future, then they are not short sighted.
|
∀x (Hardworking(x) ∧ HaveFor(x, highAmbition, future) ∧ HaveFor(x, goal, future) → ¬ShortSighted(x))
|
John is not either a hardworking individual with high ambitions and goals for the future or has a flexible schedule.
|
¬((Hardworking(john) ∧ HaveFor(john, highAmbition, future) ∧ HaveFor(john, goal, future)) ⊕ FlexibleSchedule(john))
|
John is short sighted.
|
Organized(john)
|
John chooses what he want to do with his time.
|
ChooseWhatToDoWith(john, time)
|
John is either a hardworking individual with high ambitions and goals for the future or is short sighted.
|
(Hardworking(john) ∧ HaveFor(john, highAmbition, future) ∧ HaveFor(john, goal, future)) ⊕ ShortSighted(john)
|
Ableton has an office in Germany.
|
OfficeIn(ableton, germany)
|
Ableton has an office in the USA.
|
OfficeIn(ableton, unitedStates)
|
USA and Germany are different countries.
|
¬SameCountry(germany, unitedStates)
|
Any company that has offices in different countries is a multinational company.
|
∀x ∀y ∀z (OfficeIn(x, y) ∧ OfficeIn(x, z) ∧ (¬SameCountry(y, z)) → MultinationalCompany(x))
|
Ableton makes music software.
|
MakesMusicSoftware(ableton)
|
Ableton is a multinational company.
|
MultinationalCompany(ableton)
|
Ableton makes AI software.
|
MakesAISoftware(ableton)
|
Ableton does not have an office in Germany.
|
¬OfficeIn(ableton, germany)
|
Those who can fly over a vast distance glide in the air.
|
∀x (FlyOver(x, vastDistance) → GlideInAir(x))
|
Flightless birds cannot fly over a vast distance.
|
∀x (Flightless(x) ∧ Bird(x) → ¬FlyOver(x, vastDistance))
|
Penguins are flightless birds.
|
∀x (Penguin(x) → Flightless(x) ∧ Bird(x))
|
Nonflying birds in Antarctica are penguins.
|
∀x (NonFlying(x) ∧ Bird(x) ∧ In(x, antarctica) → Penguin(x))
|
Fido is a penguin, or flies over a vast distance.
|
Penguin(fido) ∨ FlyOver(fido, vastDistance)
|
Fido is a flightless bird
|
Flightless(fido) ∧ Bird(fido)
|
Fido is not a nonflying bird in Antarctica, and he cannot glid in the air.
|
¬(NonFlying(fido) ∧ Bird(fido) ∧ In(fido, antarctica)) ∧ ¬GlideInAir(fido)
|
If Fido either can fly over a vast distance or cannot fly over a vast distance, then Fido is a nonflying bird in Antartica.
|
(FlyOver(fido, vastDistance) ⊕ ¬FlyOver(fido, vastDistance)) → (NonFlying(fido) ∧ Bird(fido) ∧ In(fido, antarctica))
|
All members of the university faculty are professors.
|
∀x (MemberOf(x, universityFaculty) → Professor(x))
|
All principal investigators are members of the university faculty.
|
∀x (PrincipalInvestigator(x) → MemberOf(x, universityFaculty))
|
No professor is also an undergraduate student.
|
∀x (Professor(x) → ¬UndergraduateStudent(x))
|
Anyone pursuing a bachelor's degree is an undergraduate student.
|
∀x (Pursuing(x, bachelor) → UndergraduateStudent(x))
|
Leon is not pursuing a bachelor's degree, and he is not a principal investigator.
|
¬(Pursuing(leon, bachelor) ⊕ PrincipalInvestigator(leon))
|
If Leon is not pursuing a bachelor's degree, then he is a professor.
|
¬Pursuing(leon, bachelor) → Professor(leon)
|
Leon is a member of university faculty.
|
MemberOf(leon, universityFaculty)
|
Leon is neither an undergraduate student nor a principal investigator.
|
¬UndergraduateStudent(leon) ∧ ¬PrincipalInvestigator(leon)
|
If leon is not a principal investigator, then Leon is an undergraduate student.
|
¬PrincipalInvestigator(leon) → UndergraduateStudent(leon)
|
A cutman is responsible for preventing and treating physical damage to a fighter.
|
∀x (Cutman(x) → Prevent(x, physicalDamageToAFighter) ∧ Treat(x, physicalDamageToAFighter))
|
Cutmen appear in boxing matches, kickboxing matches, or mixed martial arts matches bout.
|
∀x (Cutman(x) → AppearIn(x, boxingMatch) ∨ AppearIn(x, kickboxingMatch) ∨ AppearIn(x, mixedMartialArtsMatchBout))
|
Cutmen handle swelling, nosebleeds and lacerations.
|
∀x (Cutman(x) → Handle(x, swelling) ∧ Handle(x, nosebleed) ∧ Handle(x, laceration))
|
Jack is a cutman.
|
Cutman(jack)
|
No cutmen appear in boxing matches.
|
¬(∃x (Cutman(x) ∧ AppearIn(x, boxingMatch)))
|
If someone is not a cutman, then they cannot handle nosebleeds.
|
∀x (¬Cutman(x) → ¬Handle(x, nosebleed))
|
Jack is responsible for treating physical damage to a fighter.
|
Treat(jack, physicalDamageToAFighter)
|
The Mona Lisa is a world's best-known painting.
|
Painting(monaLisa) ∧ TheWorldsBestKnown(monaLisa)
|
The Mona Lisa is a portrait painted by Leonardo da Vinci.
|
PaintedBy(monaLisa, leonardodaVinci) ∧ Portrait(monaLisa)
|
Leonardo da Vinci was a scientist and painter.
|
Scientist(leonardodaVinci) ∧ Painter(leonardodaVinci)
|
Painting genres can be history, portrait, animal, landscape, and still life.
|
∀x (Painting(x) → (History(x) ∨ Portrait(x) ∨ Animal(x) ∨ Landscape(x) ∨ StillLife(x)))
|
A world's best-known artwork is painted by a scientist.
|
∃x ∃y (Painting(x) ∧ TheWorldsBestKnown(x) ∧ PaintedBy(x, y) ∧ Scientist(y))
|
Leonardo da Vinci has artworks in the landscape genre.
|
∃x (PaintedBy(x, leonardodaVinci) ∧ Landscape(x))
|
No world's best-known artworks are portraits.
|
∀x (WorldsBestKnown(x) → ¬Portrait(x))
|
No professional tennis umpires are professional tennis players.
|
∀x (ProfessionalTennisUmpire(x) → ¬ProfessionalTennisPlayer(x))
|
If you are a World Tour player, then you are a professional tennis player.
|
∀x (WorldTourPlayer(x) → ProfessionalTennisPlayer(x))
|
All Grand Slam champions are World Tour players.
|
∀x (GrandSlamChampion(x) → WorldTourPlayer(x))
|
All Grand Slam umpires are professional tennis umpires.
|
∀x (GrandSlamUmpire(x) → ProfessionalTennisUmpire(x))
|
Nadal is a World Tour player or a Grand Slam champion
|
WorldTourPlayer(nadal) ∨ GrandSlamChampion(nadal)
|
Nadal is a Grand Slam umpire.
|
GrandSlamUmpire(nadal)
|
Nadal is not a Grand Slam umpire.
|
¬GrandSlamUmpire(nadal)
|
Nadal is a Grand Slam champion.
|
GrandSlamChampion(nadal)
|
Nadal is neither a Grand Slam umpire nor a professional tennis umpire.
|
¬(GrandSlamUmpire(nadal) ∨ ProfessionalTennisUmpire(nadal))
|
If Nadal is a professional tennis umpire, then Nadal is a Grand Slam Umpire.
|
ProfessionalTennisUmpire(nadal) → GrandSlamUmpire(nadal)
|
If Nadal is a Grand Slam umpire or a professional tennis player, then Nadal is a Grand Slam umpire.
|
GrandSlamUmpire(nadal) ∨ ProfessionalTennisPlayer(nadal) → GrandSlamUmpire(nadal)
|
Businesses are either sanctioned or unsanctioned.
|
∀x (Buisness(x) → Sanctioned(x) ⊕ ¬Sanctioned(x))
|
Sanctioned businesses are limited.
|
∀x (Buisness(x) ∧ Sanctioned(x) → Limited(x))
|
Unsanctioned businesses are free.
|
∀x (Buisness(x) ∧ ¬Sanctioned(x) → Free(x))
|
The Crude Oil Data Exchange is a business that isn't free.
|
Buisness(crudeOilDataExchange) ∧ ¬Free(crudeOilDataExchange)
|
Crude Oil Data Exchange is sanctioned.
|
Sanctioned(crudeOilDataExchange)
|
Crude Oil Data Exchange is unsanctioned.
|
¬Sanctioned(crudeOilDataExchange)
|
Crude Oil Data Exchange is limited.
|
Limited(crudeOilDataExchange)
|
When something is depressing, it is sad.
|
∀x (Depressing(x) → Sad(x))
|
The end of a relationship is depressing.
|
Depressing(v)
|
The end of a relationship is invigorating
|
Invigorating(v)
|
Palstaves are a type of early bronze axe.
|
EarlyBronzeAge(palstave) ∧ Axe(palstave)
|
Palstaves are found in northern, western, and southwestern Europe and are cast in molds.
|
FoundIn(palstave, northernEurope) ∨ FoundIn(palstave, westernEurope) ∨ FoundIn(palstave, southWesternEurope)) ∧ CastIn(palstave, molds)
|
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