Assuming it were symmetrical would get you in trouble.

Someone cleverer than me could probably put this in the same form as these questions.

(ht K T Cat)

In q10, I can see where the supporters are going with this and there is a formalism that I am not familiar with (though I think that makes it more of a shibboleth than a neutral evaluation). I wondered in general how we are supposed to know what hasn't been assumed by the questioner. I fell into that trap. If you don't think the questioner was assuming stuff, go to q15.

For q15, though, many supporters seem to be grasping at stuff that wasn't mentioned either. (deuterium, water-like substance) We are given a straight fact, then essentially asked whether that can change. The same sort of lack of "play" that is in the word "Paris" should apply to "water" was well.

Phil, you said it well, also.

Not only I think that my answer to the question 15 (valid) was good, I think that the one presented as the "correct one" (therefore, invalid) is clearly wrong.

From the beginning, you give us premises. Some are accurate, some are not but it doesn't change anything for the test (example, question 10 is false : Paris is in New Zealand). Question 10 could have been : "A lives in X" "X is in Y" "Therefore A lives in Y".

The first premise of question 15 is : "Water is a molecule composed of two hydrogen atoms and one oxygen atom.". You give us a definition : Water is THIS. I know it may not be completly accurate in real life (as it was for Paris). Water could be defined otherwise, but in this test, we've gotta think only in function of your premises. It is easier when we use some variables : "Z is a molecule composed of two hydrogen atoms and one oxygen atom", or if you prefer : "Z is D".

The conclusion is : "Therefore we can predict that every future examination of water will reveal the same chemical composition.". My answer is : of course, yes. Because water is D, anytime we examine water it will always be D. If it isn't, that would mean that the substance examined wasn't water, because de premise define it by is chemical composition. See it that way :
a) Z is D
b) Every observations or examination as confirmed that Z is D (superfluous, from the beginning, premises don't have to be confirmed, we're only evaluating their link to the conclusion)

Conclusion : Therefore we can predict that every future examination of Z will reveal that it is D. (of course, conclusion is premise a).

In the explication of your answer, you write : "However, it is possible also that there may exist a substance that looks like water, boils as water, freezes as water, nourishes plants and life as water, and yet has a different chemical composition to what we know as water." Then, it would simply not be water as defined in the premise a). Therefore, it wouldn't be an examination of water (or Z). You use the expression "to what we know as water". As I said, we only know what is in the premise, same thing than Paris in New Zealand.

I strongly suggest that you review your position.

This discussion has been so fascinating, and also kind of a mess, because the test is for "validity", undefined in the test instructions, and the questions are from (at least) syllogistic, propositional, and inductive logic. The notion of a valid argument is different for those kinds of logical argument.

I got 100% easily, with very little thought on each question - because I have studied logic in school, and could easily see each question for what it wanted. It is easy to see in the comments how people who haven't had big spoonfuls of university logic would instead think about, e.g, whether all Paris instances had been defined, when the choice of "Paris" instead of "p" or "x" is totally irrelevant

Test takers who had not ever even known the core idea of "validity" - if the premises are true, then the conclusion must also be true - may have fallen prey to the danger from Quine that I mentioned earlier -"remember that valdity is not a term of praise" In propositional logic, validity is formalized first as the tautology - p and q; so, p. That is valid, but not very enlightening....

The converse of Quine's idea is that a praiseworthy and reasonable argument, like the perfectly reasonable #15, need not be VALID.

For question #1, if all ducks quack, the "D" circle should be completely within the "Q" circle. Showing part of the "D" circle OUTSIDE of the "Q" circle contradicts the first premise, that all ducks quack. We do not have enough information to tell whether the D circle is the same size as the Q circle (which would be the case if ONLY ducks quack) or if the D circle is smaller, but clearly D falls completely within Q. The "DO" circle should fall entirely within the D circle. Since premise A refers to ducks in the plural, and premise B refers to Donald in the singular, we can assume that the DO circle is smaller than the D circle. In either Venn diagram (D the same size as Q, or D smaller than Q), DO would fall within BOTH D and Q, and that is how we know that Donald quacks.

For answer #2, the Female Logicians circle should fall entirely within the "Clear Thinker" circle, under premise A, but again we don't know whether they are the same size, or whether the Female Logicians circle is smaller (we don't know whether all Clear Thinkers are Female Logicians). Similarly, the Lawyers circle should fall entirely within the "Clear Thinker" circle, under premise B, but again we don't know whether they are the same size, or whether the Lawyers circle is smaller (we don't know whether all Clear Thinkers are Lawyers). Since Female Logicians and Lawyers could each be smaller circles, both entirely within the Clear Thinkers circle, we do not even know whether the Female Logicians and Lawyers circles intersect at all. It is possible that NO Female Logicians are Lawyers. All we know is that the premises are clearly not sufficient to support the conclusion that all Female Logicians are Lawyers.

I got a 93%. Guess which question I missed? I was offended. I couldn't be wrong. In the end, we all took either a very poorly written quiz (as per the craptacular explanation given for 15) or a maddeningly deliberate, devilishly clever quiz (ego stroke, I don't like feeling dumb). If the former is the case, I'm mad I wasted my time. If the latter is true, being wrong made me a better person. Screw it, I'm just mad at being a better person minus two hours of sleep.

Here's my take (after looking at all other comments):

I am an objective observer.
I know that (as given by the quiz):

A)Water is made of 2 H and 1 O (fact, as given)

B)Some people (mostly unaware of the above fact, although these people could include you) have consistently observed water to be made of 2 H and 1 O with a microscope (a tool)

Conclusion
Therefore we (I, in my or your case) CAN predict (accurately or not necessarily so?) that every future examination of water (with or without a tool?; naked eye maybe?) will reveal the same chemical composition.

One could argue that by definition (which is subjective), a prediction does not have to be accurate. All done. It's valid. Who cares about the fact that the means of examination are not explained.

What about the word 'can'? I can drive. I can eat. I can even drink (I'm 21, but if I wasn't, I still could). I can do a lot of things.

can-
1. to be able to; have the ability, power, or skill to: She can solve the problem easily, I'm sure.
2. to know how to: He can play chess, although he's not particularly good at it.
3. to have the power or means to: A dictator can impose his will on the people.
4. to have the right or qualifications to: He can change whatever he wishes in the script.
5. may; have permission to: Can I speak to you for a moment?
6. to have the possibility: A coin can land on either side.

'Can' is not a logical verb. 'Is', well, is a logical verb. The statement is invalid because of this, I think. Wait, am I right? Is this logic correct? Does that disqualify the statement? Maybe it doesn't. Does the fact that I am so fixated on the 'can' mean that I was using too much of what I know and not enough simple logic? Are the semantics of a logic question distracting, or the only reason a logic question is what it is?

Is question 15 a philosophical one? Probably not, but it's the only way I can justify spending two hours thinking about this crap question

Shenanigans on the water one.

But Venn diagrams are named after John Venn, not Charles.

I happen to know this after research for my own book, Venn That Tune: Bringing the Poetry of Maths to the Magic of Pop, which fans of logic might enjoy.

http://www.vennthattune.com

#15 - Given that in the Conclusion he just generalized with 'every future examination' I chose to consider the possibility that future examination methods and equipment might reveal a more complex structure to the water molecule than is presently discernible by present examination methods and equipment.

His argument for the possible existence of a 'water-like in every way but composition' substance is irrelevant because the question specifically indicates water as the substance of concern. By saying that a possible substance is water-like, but different in composition, you're by your own description not talking about water, and so not talking about the substance mentioned in the question.

Some of these comments/arguments are priceless. The whole exercise becomes a rorschach if mistakes are made.

Chemical composition is fixed. Water is H2O every single time. The quibble about heavy water is irrelevant - deuterium is still hydrogen. It is just another isotope of hydrogen, just as uranium-235 and uranium-238 are both still uranium. As for "don't drink it" - I've drunk heavy water before. So have you. It is present in almost all water on this planet.

The statements in question 15:
"a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition."

a.) refers to the composition of water molecules
b.) provides supporting evidence for a.)
The conclusion refers to the composition of water molecules.

The given answer then takes a tangent and refers to chemical properties of water, which are not once raised in the initial statements. In point of fact, if I examine water I will always discover H2O molecules. If I examine "water" and do not find H2O, then I am not examining water at all. The chemical properties are irrelevant, water is H2O and nothing else.

To reach the answer given, the conclusion should have read:
"We can predict that if we examine a substance with the same chemical properties as water, that substance will have the chemical composition H2O".
This would also have required some establishing statements regarding the chemical properties of water.

There is also the issue that "we can predict" has no bearing on the accuracy of the prediction. I can predict that the core of the planet Jupiter is made of strawberries. I can also predict that it will snow in the Sahara Desert tomorrow. The accuracy of those predictions is not relevant to the fact that I can actually make those predictions.

The second predicate is: b) Every observation or examination by microscope has confirmed this

The second predicate therefore means that WATER is being observed under a microscope to reveal the chemical composition, not some other substance that behaves and looks like water.

1: A is in B
2: B is in C
3: A is in C

Impossible to deny this validity. Forget about the fact that there is a Paris France, or Paris anywhere. The word "Paris" doesn't mean anything and/or it means everything. In this example, Paris could mean "a continent on the planet New Zealand" - it doesn't matter. The form is valid, he did not introduce any known new variables. There is absolutely no justification to believe that "Paris" in premise 1 and 2 are different. If there was, then you surely got almost every other valid questions wrong.

It's like saying this is invalid:
1: All Ducks Quack
2: Donald is a Duck
3: Donald Quacks

Because "Duck" in premise 2 could mean something that the author didn't define and is trying to trick us. Maybe "Duck" means, plastic rubber duckies, aye?

I can understand people being frustrated for not understanding the water one. But to deny the validity of the Paris one is just insane. Chaos even.

i = 1
i + i = 3... the second i really is a 2, tricked you!

Lew

P.S.
Water:
1: A (water) is B (H20)
2: C (every past examination) shows A is B
3: D (every future examination) will show A is B

Too many variables, none of which are connected. That's one reason why it's invalid. There are probably several.

As for the test proposed by Steve L:

A: Exactly one of Statements B and C (below) is false
B: Statement C is false
C: Statement A is false

Conclusion: Statement B is true.

Invalid or valid?

Valid.

The logic for each statement is laid out:
A: True = B or C (but not both) must be false, False = B and C may be both true or both false
B: True = C must be false, False = C must be True (A must be false)
C: True = A must be false, False = A must be True

Now for the combinations:
A: False = B and C may be both true or both false
B: False = C must be true
C: False = A must be true
- C cannot be true and false. Fail.

A: False = B and C may be both true or both false
B: False = C must be true
C: True = A must be false
- All conditions are met. However, the states of B and C make that A true, but it is not. Fail.

A: False = B and C may be both true or both false
B: True = C must be false
C: False = A must be true
- All conditions are met. However, the states of B and C make that A true, but it is not. Fail.

A: False = B and C may be both true or both false
B: True = C must be false
C: True = A must be false
- C cannot be True *and* false. Fail.

A: True = B or C (but not both) must be false
B: False = C must be true
C: False = A must be true
- Given the states of B & C, A cannot be true. Fail.

A: True = B or C (but not both) must be false
B: False = C must be true
C: True = A must be false
- A cannot be true and false. Fail.

A: True = B or C (but not both) must be false
B: True = C must be false
C: False = A must be true
- B is True and C is False, passes condition A. C is false, passes condition B. A is true, passes condition C (as modified by B). All conditions are met. Pass.

A: True = B or C (but not both) must be false
B: True = C must be false
C: True = A must be false
- A cannot be true and False, C cannot be true and false. Fail.

Only one condition passes it's internal logic.
A=True, B=True, C=False. Therefore, the conclusion is valid.

B: Statement C is false

C: Statement A is false

Conclusion: Statement B is true.

Invalid or valid?

Invalid, if Statement B is true then Statement C would have to be false so Statement A would be true - BUT, if statement A is false then Statement C would have to be true and Statement B would be false.

The question is:
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition.

Her answer is:
Invalid. Invalid but controversial in philosophical circles. If one defines water as a property that contains two atoms of hydrogen and one atom of oxygen only, then the argument above is valid. However, it is possible also that there may exist a substance that looks like water, boils as water, freezes as water, nourishes plants and life as water, and yet has a different chemical composition to what we know as water. There is nothing that could logically prevent this possibility occurring so the argument then becomes invalid.

Let's rephrase the question.
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) You observe a material that has a different chemical composition but has the same melting point, freezing point, and looks like water.

Conclusion
You are observing water.

Everyone would agree that this is an invalid conjecture.

So what we have here is someone who wrote a book on logic, included a test with a logic error, and is too embarrassed to admit it.

Taken from Wikipedia: A prediction is a statement or claim that a particular event will occur in the future in more certain terms than a forecast. The etymology of this word is Latin (from præ- "before" plus dicere "to say"). Niels Bohr stated "Prediction is very difficult, especially if it's about the future."

Nice quiz!

How about this one?

A: Exactly one of Statements B and C (below) is false

B: Statement C is false

C: Statement A is false

Conclusion: Statement B is true.

Invalid or valid?