Logic – Geometry – Direct Proofs Name______
Each of the following exercises consists of a ‘theorem’ and a proof in which two statements have been omitted. Insert the missing statements to complete the proof (QED…Q.E.D. is an abbreviation of the Latin phrase "quod erat demonstrandum" (which translates into” which was to be demonstrated").
1. Theorem: If two hungry vultures took an airplane, they would be told that there is a limit of two carrion per passenger.
Proof:
If two hungry vultures took an airplane, they would want to take along some food.
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If they tried to carry on six dead raccoons, the flight attendant would object.
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2. Theorem: If a group of chess players checked into a hotel, the manager would say, “I can’t stand chess nuts boasting in an open foyer.”
Proof:
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If they stood in the lobby bragging about their tournament victories, the manager would ask them to leave.
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If they asked why, the manager would say, “I can’t stand chess nuts boasting in an open foyer.”
3. Copy the statements, writing them if-then form and rearranging them in logical order.
i. A duck would ask for some Chapstick, if he went to a drugstore.
ii. If a duck had sore lips, he would go to a drugstore.
iii. A duck would ask to have it pit on his bill, if he asked for some Chapstick.
4. Copy the statements, rearranging them in logical order. What ‘theorem’ do they prove?
i. If you take a plan, you will go to the airport
ii. If you go to Dallas, you will take a plane.
iii. If you see all the cabs lined up, you will see the yellow rows of taxis.
iv. If you go to the airport, you will see all the cabs lined up.
5. The artist Rube Goldberg was well known for his ridiculous inventions and today his name is associated with any complicated and impractical way of performing a simple task. He was in fact an engineer who felt many people managed to do things the hard way. If one assumes the following series of events are likely (i.e. Honda commercial), what is the theorem of this preposterous chain of events?
· If you raise the spoon of soup to your mouth, the string is pulled.
· If the string is pulled, the ladle is jerked.
· If the ladle is jerked, it throws a cracker past the parrot.
· If the cracker goes pasts the parrot, the parrot tilts his perch.
· If the parrot tilts his perch, he upsets the seeds into a pail.
· When the seeds are upset into a pail, extra weight pulls a cord which opens and lights an automatic cigar lighter.
· If the cigar is lit, then it sets off a skyrocket which causes the sickle to cut the string.
· After the sickle cuts the string, the clock pendulum with a napkin swings back and forth wiping off the man’s chin.
therefore ______
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6. The following statements appear on the customer agreement for obtaining a credit card.
· A transaction finance charge is a charge made if a new advance is added to your account.
· If you go over your credit limit, you will be charged a fee.
· A supercheck is a check designed for use with your credit card account.
· If you are charged a fee, the fee will be added to your balance.
· If your card is lost or stolen, you agree to report it immediately.
a) Which statements are definitions and what words do they define?
b) Which statements are postulates?
c) Which two statements can be combined to form a syllogism?
d) What theorem is proved by the syllogism?
7. Rearrange the conditionals. What theorem is proved?
· If you don’t do well in this class, then you don’t like proofs.
· If you love Geometry, then you like proofs.
· If you do well in this class, then you will get an A.
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Therefore:______
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8. Rearrange the conditionals. What theorem is proved?
· He will run, if the ghosts chase Scooby Doo.
· Scooby Doo will find the Scooby snacks, if Shaggy follows Scooby Doo.
· If Scooby Doo finds the Scooby snacks, then Scooby will share with Shaggy.
· If Scooby Doo asks for Scooby Doo snacks, then the ghosts will chase him.
· If Scooby Doo runs, then Shaggy will follow him.
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Therefore:______
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9. Rearrange the conditionals. What theorem is proved?
· If N’SYNC’s fans don’t start dancing, then the floor will not shake.
· If N’SYNC starts singing “Bye Bye Bye”, then the fans will start dancing to it.
· N’SYNC will not break down some moves, if the fans don’t scream.
· If N’SYNC break down some moves, then the fans will go crazy.
· The fans will scream louder, if the floor shakes.
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Therefore:______
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