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## Question

puzzle in book:all but 2 of my cars a fords all but 2 of my cars are toyotas and all but 2 of my cars are hondas how many cars do i have

3 cars

couldnt he have 2 cars and none of them be a honda toyota or ford?

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I say (again) that not only does the phrase 'all but' imply a non-empty set, it implies a set of greater value than the figure mentioned after it. In this case it's 2, so the set must be greater than 2. Given that, the answer must be 3.

You of course can say that All but 2 implies an initial set of 3 or more.

Anyone is free to define rules, and publish them, about the meaning of statements.

Under any set of rules [a sufficiently complete set] there can be a meaningful discussion.

In this case, you and Aristotle could talk. Oh, wait. That poses a different problem.

In geometry it was once believed that from other axioms it could be proved

that two parallel lines do not cross. But attempts at that proof failed.

So they added it as an axiom.

Geometries with that axiom are called Euclidean geometries.

Then someone said, well, what if we don't have that axiom?

Omitting that axiom defines other [equally valid, non-Euclidean] geometries [e.g. hyperbolic.]

In logic, ascribing existential import to All [or not] connotes Aristotelian or [non-Aristotelian] Boolean logic.

You don't have to "buy" either of them. You choose one, and use it.

Neither of them is invalidated by the presence of the other.

The French language is not invalidated by the presence of the Russian language.

To have a meaningful discussion participants need little more than

1. definition of terms [vocabulary with an agreed upon dictionary]
2. agreed upon rules of grammar and syntax.
If participants agree on these, there can be a meaningful exchange.

I think that in my very first post in this thread I said that both answers to the OP question are acceptable.

One carries the Aristotelian interpretation; the other, Boolean.

Some of the discussions here are rather like Americans,

who insist that "bum" means "hobo", arguing with Brits,

who are adamant that it means something quite different!

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The book is correct. 3 is the answer. "All but..." refers to at least one. Therefore, "all but 2 of my cars are ____" translates into "At least 1 car is THIS, 2 are not". So, at least 1 car is a Ford, 2 are not. At least 1 car is a Toyota, 2 are not. At least 1 car is a Honda, 2 are not. Add em' up and viola! You have 3 cars. Simple ;-)

Itachi-San.

Here is someone you can talk to.

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An empty set is a perfectly valid notion. You can have an empty set of Fords. (I do.) I think, what causes the outrage here, is that the anwer 2 cars assigns the names to the members of an empty set. I.e., I have an empty set and its members are named Ford.

Edited by Prime

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Is anyone else here a programmer? Without the use of empty sets, most computer logic won't work.

If you have ever tried writing info to an (supposedly) empty array that already has an element you know what I mean .

Edited by pw0nzd

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puzzle in book:all but 2 of my cars a fords all but 2 of my cars are toyotas and all but 2 of my cars are hondas how many cars do i have

3 cars

couldnt he have 2 cars and none of them be a honda toyota or ford?

the correct answer is 3 because it names three brands of cars 1. ford 2. toyotas 3. hondas now to the riddle its self all but two of my cars are fords meaning toyota and honda all but 2 of my cars are toyotas meaning honda and ford all of my cars are honda but two meaning toyota and ford so this means he has 3 cars because he says only 2 are not ford and 2 are not toyotas and two are not hondas so that mean there are only two other brands with only two units to fill evenly. soo youre crazy ( just joking )

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the correct answer is 3 because it names three brands of cars 1. ford 2. toyotas 3. hondas now to the riddle its self all but two of my cars are fords meaning toyota and honda all but 2 of my cars are toyotas meaning honda and ford all of my cars are honda but two meaning toyota and ford so this means he has 3 cars because he says only 2 are not ford and 2 are not toyotas and two are not hondas so that mean there are only two other brands with only two units to fill evenly. soo youre crazy ( just joking )

Hi brainz,

You showed that 3 is "a correct answer".

You did not show it is "the correct answer".

"couldnt he have 2 cars and none of them be a honda toyota or ford?"

In other words, if there can be more than one correct answer, is 2 one of them?

Try to show that 3 is the only possible answer.

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Just my opinion of the whole 'All implies at least one' debate.

With respect to sets of things, to say 'all' items in a set satisfy a condition is simply saying that the number of items in a set which satisfy a condition is equal to the total number of items in the set. For a set of size 5, 'All' implies 5 items satisfy the condition. For a set of size 100, 'All' implies 100 items satisfy the condition. For a set of size zero, the empty set, 'All' implies 0 items match the condition, which will always be true. Kind of like how multiplication by zero always yields zero, regardless of the other value.

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