A simple logical reasoning test

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It excludes "all". Definition of almost is "very nearly but not entirely" - it specifically means not all (but nearly). If you "almost" catch a train, it means you didn't catch the train.

Last edited by edgewaters on 13 Jul 2012, 3:48 am, edited 1 time in total.

I'd have no logical reasoning to bring up this test with someone I'm dating. Their logic would be to show me the door if I did.

As I said, studying mathematics has ruined my intuition about certain logical connectives. In mathematics, "or" includes "and", and "almost all" includes "all".

For example, the following mathematical statements are true:





The first one is true even though 0 satisfies both constraints, since "A or B" is interpreted as "[A and not B] or [B and not A] or [A and B]".

The second one is true since "almost all things which are in the set X are also in the set Y" is interpreted as "using the obvious measure on the set X, the set of things which are in X and not in Y has measure zero", and the empty set has measure zero using the obvious measure on the positive integers.

I'm terrible at math, but:

In set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many.

http://en.wikipedia.org/wiki/Almost

In mathematics, a finite set is a set that has a finite number of elements. For example,

{2,4,6,8,10}

is a finite set with five elements. The number of elements of a finite set is a natural number

http://en.wikipedia.org/wiki/Finite_set

There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, with the latter definition first appearing in the 19th century. Some authors use the term "natural number" to exclude zero and "whole number" to include it; others use "whole number" in a way that excludes zero, or in a way that includes both zero and the negative integers.

http://en.wikipedia.org/wiki/Natural_number

We await your continuation.

Well spotted, but that is just the result of editors working on different pages having different definitions of "natural number". Every mathematician will agree that the empty set is finite.

Your definition of "almost all" is actually distinct from my definition of "almost all", since the obvious measure on the positive integers is a measure called the counting measure, and in the counting measure, only the empty set has measure zero, and other finite sets have positive measure.

Actually, there is even a third way we could interpret "almost all" in this case, since there is a special notion for the positive integers called natural density, and we could interpret "almost all positive integers are positive" to mean "the set of positive integers which are not positive has natural density zero".

However, it doesn't matter which way we interpret "almost all" in this case; the statement "almost all positive integers are positive" is true in all three cases. To summarise:

If we interpret "almost all positive integers are positive" to mean "the set of positive integers which are not positive is finite", then it is true that "almost all positive integers are positive", since the empty set is finite.

On the other hand, if we interpret "almost all positive integers are positive" to mean "using the counting measure on the positive integers, the set of positive integers which are not positive has measure zero", then it is true that "almost all positive integers are positive", since the empty set has measure zero using the counting measure on the positive integers.

Finally, if we interpret "almost all positive integers are positive" to mean "the set of positive integers which are not positive has natural density zero", then it is true that "almost all positive integers are positive", since the empty set has natural density zero.

Yep, that's what I was referring to.

truth

I also like it for this section because:

People who missed the word therefore, and therefore, did not arrive at the answers "False, True, False" should not date X.
X should not date Q.
All Q are people(P) but not all people(P) are Q.
J should never date T.
The X's are wondering what Q, J, and T are.

Most people, do not appreciate the value of X.

Apparently, this is why it's so hard for Aspies to get a date.

Obviously...

PI'll fix my errors of wording tomorrow; it's too much typing on my phone and if I turn my computer on I'll be up all night.


I'll clarify one thing: in these examples, "false" should be taken to mean "definitely not", and "not enough information to tell" should be taken to mean "not necessarily".
For example, for me to state "I am dead" is, at the time of writing, false.
However, if I were to state "I will die tomorrow", the answer to that would be "not necessarily", as there is insufficient information to predict my death, or lack of.

Yes, it was a typo.
I know 10-year-old children who could pass that test without so much quibbling; it's kind of depressing that such basic reasoning skills need to actually be taught in year 12.

stop it now, you "typo" too much Clear it up in the morning

Yes, exactly.
If I get almost all the answers correct on a test, it means I got some wrong. However, without further information, you can't conclude that I got any specific answer right or wrong.

Whoosh! Right over my head. I suck at math.

But ...



Apparently I'm not bad at math for lack of deductive reasoning ... which seems to have been "almost" (hehe) absent in this thread, since so few were able to deduce the typo.

I fixed it! My phone decided that I meant a different word than the one I wanted.
You're just too quick; that's why you spotted it before I could edit it.