** 2.** Consider the following axioms:

- Every child loves Santa.

*&forall x (CHILD(x) &rarr LOVES(x,Santa))* - Everyone who loves Santa loves any reindeer.

*&forall x (LOVES(x,Santa) &rarr &forall y (REINDEER(y) &rarr LOVES(x,y)))* - Rudolph is a reindeer, and Rudolph has a red nose.

*REINDEER(Rudolph) &and REDNOSE(Rudolph)* - Anything which has a red nose is weird or is a clown.

*&forall x (REDNOSE(x) &rarr WEIRD(x) &or CLOWN(x))* - No reindeer is a clown.

*¬ &exist x (REINDEER(x) &and CLOWN(x))* - Scrooge does not love anything which is weird.

*&forall x (WEIRD(x) &rarr ¬ LOVES(Scrooge,x))* - (Conclusion) Scrooge is not a child.

*¬ CHILD(Scrooge)*

** 3.** Consider the following axioms:

- Anyone who buys carrots by the bushel owns either a rabbit or a
grocery store.

*&forall x (BUY(x) &rarr &exist y (OWNS(x,y) &and (RABBIT(y) &or GROCERY(y))))* - Every dog chases some rabbit.

*&forall x (DOG(x) &rarr &exist y (RABBIT(y) &and CHASE(x,y)))* - Mary buys carrots by the bushel.

*BUY(Mary)* - Anyone who owns a rabbit hates anything that chases any rabbit.

*&forall x &forall y (OWNS(x,y) &and RABBIT(y) &rarr &forall z &forall w (RABBIT(w) &and CHASE(z,w) &rarr HATES(x,z)))* - John owns a dog.

*&exist x (DOG(x) &and OWNS(John,x))* - Someone who hates something owned by another person will not date
that person.

*&forall x &forall y &forall z (OWNS(y,z) &and HATES(x,z) &rarr ¬ DATE(x,y))* - (Conclusion) If Mary does not own a grocery store, she will not date
John.

*(( ¬ &exist x (GROCERY(x) &and OWN(Mary,x))) &rarr ¬ DATE(Mary,John))*

** 4.** Consider the following axioms:

- Every Austinite who is not conservative loves some armadillo.

*&forall x (AUSTINITE(x) &and ¬ CONSERVATIVE(x) &rarr &exist y (ARMADILLO(y) &and LOVES(x,y)))* - Anyone who wears maroon-and-white shirts is an Aggie.

*&forall x (WEARS(x) &rarr AGGIE(x))* - Every Aggie loves every dog.

*&forall x (AGGIE(x) &rarr &forall y (DOG(y) &rarr LOVES(x,y)))* - Nobody who loves every dog loves any armadillo.

*¬ &exist x ((&forall y (DOG(y) &rarr LOVES(x,y))) &and &exist z (ARMADILLO(z) &and LOVES(x,z)))* - Clem is an Austinite, and Clem wears maroon-and-white shirts.

*AUSTINITE(Clem) &and WEARS(Clem)* - (Conclusion) Is there a conservative Austinite?

*&exist x (AUSTINITE(x) &and CONSERVATIVE(x))*

( ( (not (Austinite x)) (Conservative x) (Armadillo (f x)) ) ( (not (Austinite x)) (Conservative x) (Loves x (f x)) ) ( (not (Wears x)) (Aggie x) ) ( (not (Aggie x)) (not (Dog y)) (Loves x y) ) ( (Dog (g x)) (not (Armadillo z)) (not (Loves x z)) ) ( (not (Loves x (g x))) (not (Armadillo z)) (not (Loves x z)) ) ( (Austinite (Clem)) ) ( (Wears (Clem)) ) ( (not (Conservative x)) (not (Austinite x)) ) )

** 5.** Consider the following axioms:

- Anyone whom Mary loves is a football star.

*&forall x (LOVES(Mary,x) &rarr STAR(x))* - Any student who does not pass does not play.

*&forall x (STUDENT(x) &and ¬ PASS(x) &rarr ¬ PLAY(x))* - John is a student.

*STUDENT(John)* - Any student who does not study does not pass.

*&forall x (STUDENT(x) &and ¬ STUDY(x) &rarr ¬ PASS(x))* - Anyone who does not play is not a football star.

*&forall x (¬ PLAY(x) &rarr ¬ STAR(x))* - (Conclusion) If John does not study, then Mary does not love John.

*¬ STUDY(John) &rarr ¬ LOVES(Mary,John)*

** 6.** Consider the following axioms:

- Every coyote chases some roadrunner.

*&forall x (COYOTE(x) &rarr &exist y (RR(y) &and CHASE(x,y)))* - Every roadrunner who says ``beep-beep'' is smart.

*&forall x (RR(x) &and BEEP(x) &rarr SMART(x))* - No coyote catches any smart roadrunner.

*¬ &exist x &exist y (COYOTE(x) &and RR(y) &and SMART(y) &and CATCH(x,y))* - Any coyote who chases some roadrunner but does not
catch it is frustrated.

*&forall x (COYOTE(x) &and &exist y (RR(y) &and CHASE(x,y) &and ¬ CATCH(x,y)) &rarr FRUSTRATED(x))* - (Conclusion) If all roadrunners say ``beep-beep'', then all coyotes
are frustrated.

*(&forall x (RR(x) &rarr BEEP(x)) &rarr (&forall y (COYOTE(y) &rarr FRUSTRATED(y)))*

( ( (not (Coyote x)) (RR (f x)) ) ( (not (Coyote x)) (Chase x (f x)) ) ( (not (RR x)) (not (Beep x)) (Smart x) ) ( (not (Coyote x)) (not (RR y)) (not (Smart y)) (not (Catch x y)) ) ( (not (Coyote x)) (not (RR y)) (not (Chase x y)) (Catch x y) (Frustrated x) ) ( (not (RR x)) (Beep x) ) ( (Coyote (a)) ) ( (not (Frustrated (a))) ) )

** 7.** Consider the following axioms:

- Anyone who rides any Harley is a rough character.

*&forall x ((&exist y (HARLEY(y) &and RIDES(x,y))) &rarr ROUGH(x))* - Every biker rides [something that is] either a Harley or a BMW.

*&forall x (BIKER(x) &rarr &exist y ((HARLEY(y) &or BMW(y)) &and RIDES(x,y)))* - Anyone who rides any BMW is a yuppie.

*&forall x &forall y (RIDES(x,y) &and BMW(y) &rarr YUPPIE(x))* - Every yuppie is a lawyer.

*&forall x (YUPPIE(x) &rarr LAWYER(x))* - Any nice girl does not date anyone who is a rough character.

*&forall x &forall y (NICE(x) &and ROUGH(y) &rarr ¬ DATE(x,y))* - Mary is a nice girl, and John is a biker.

*NICE(Mary) &and BIKER(John)* - (Conclusion) If John is not a lawyer, then Mary does not date John.

*¬ LAWYER(John) &rarr ¬ DATE(Mary,John)*

** 8.** Consider the following axioms:

- Every child loves anyone who gives the child any present.

*&forall x &forall y &forall z (CHILD(x) &and PRESENT(y) &and GIVE(z,y,x) &rarr LOVES(x,z)* - Every child will be given some present by Santa if Santa
can travel on Christmas eve.

*TRAVEL(Santa,Christmas) &rarr &forall x (CHILD(x) &rarr &exist y (PRESENT(y) &and GIVE(Santa,y,x)))* - It is foggy on Christmas eve.

*FOGGY(Christmas)* - Anytime it is foggy, anyone can travel if he has some
source of light.

*&forall x &forall t (FOGGY(t) &rarr ( &exist y (LIGHT(y) &and HAS(x,y)) &rarr TRAVEL(x,t)))* - Any reindeer with a red nose is a source of light.

*&forall x (RNR(x) &rarr LIGHT(x))* - (Conclusion) If Santa has some reindeer with a red nose, then
every child loves Santa.

*( &exist x (RNR(x) &and HAS(Santa,x))) &rarr &forall y (CHILD(y) &rarr LOVES(y,Santa))*

** 9.** Consider the following axioms:

- Every investor bought [something that is] stocks or bonds.

*&forall x (INVESTOR(x) &rarr &exist y ((STOCK(y) &or BOND(y)) &and BUY(x,y)))* - If the Dow-Jones Average crashes, then all stocks that are
not gold stocks fall.

*DJCRASH &rarr &forall x ((STOCK(x) &and ¬ GOLD(x)) &rarr FALL(x))* - If the T-Bill interest rate rises, then all bonds fall.

*TBRISE &rarr &forall x (BOND(x) &rarr FALL(x))* - Every investor who bought something that falls is not happy.

*&forall x &forall y (INVESTOR(x) &and BUY(x,y) &and FALL(y) &rarr ¬ HAPPY(x))* - (Conclusion) If the Dow-Jones Average crashes and the T-Bill
interest rate rises, then any investor who is happy bought some gold stock.

*( DJCRASH &and TBRISE ) &rarr &forall x (INVESTOR(x) &and HAPPY(x) &rarr &exist y (GOLD(y) &and BUY(x,y)))*

** 10.** Consider the following axioms:

- Every child loves every candy.

*&forall x &forall y (CHILD(x) &and CANDY(y) &rarr LOVES(x,y))* - Anyone who loves some candy is not a nutrition fanatic.

*&forall x ( (&exist y (CANDY(y) &and LOVES(x,y))) &rarr ¬ FANATIC(x))* - Anyone who eats any pumpkin is a nutrition fanatic.

*&forall x ((&exist y (PUMPKIN(y) &and EAT(x,y))) &rarr FANATIC(x))* - Anyone who buys any pumpkin either carves it or eats it.

*&forall x &forall y (PUMPKIN(y) &and BUY(x,y) &rarr CARVE(x,y) &or EAT(x,y))* - John buys a pumpkin.

*&exist x (PUMPKIN(x) &and BUY(John,x))* - Lifesavers is a candy.

*CANDY(Lifesavers)* - (Conclusion) If John is a child, then John carves some pumpkin.

*CHILD(John) &rarr &exist x (PUMPKIN(x) &and CARVE(John,x))*

Gordon S. Novak Jr.