Viral Logic Test from Brazil.

[JoeMoma]

My Answer. I would have to add option F --> none of the above at the bottom of the list.

To explain why I believe that the narrator's explanation is incorrect: "All my hats are green" is not a conditional statement so "vacuously true" does not apply. Let say I'm Pinocchio. In order for all my hats to be green, I must have hats. The hats must exist for the statement to be true. A nonexistent hat cannot have the attribute of being green (zero hats). Thus answer C is possibly correct; however, we cannot conclude that answer C ( 0 hats) is the correct answer unless that is the only way the statement can be a lie. Since answer A (at least one hat) is also possibly if there is a non-green hat, we cannot conclude either A or C alone. Talso, the other answers are incorrect for the reasons stated in the video.

Had Pinocchio said "If I have hats, then all my hats are green" , then "vacuously true" would apply since the premise of "I have hats" was not met to begin with, so there is no determination of the conclusion "All my hats are green" if there are no hats. The statement "All my hats are green" does not establish a premise of a conditional statement, so "vacuously true" does not apply. Notice the example of "All the mobile phones in the room are turned off" also does not establish a premise of a conditional statement, so "vacuously true" does not apply to that statement either. A mobile phone must exist to have the state of being either turned on or turned off. Zero mobile phones cannot be in the state of turned on or turned off because there is no phone.

And one more thing, being a math ol

 

[JoeMoma]

Depends what you mean by "always lies".
If you say "My brother's name is John", where is the lie? Or is all of it a lie?

He didn't say he has or doesn't have a brother. So he's not lying.
Therefore when saying "all of my hats are green", doesn't mean he has hats, or that he doesn't have hats. We can't conclude anything from that at all.

All we can conclude is that whatever hats he may have, one isn't green. Nothing more.

If he has no brother, then his brother's name is not John. Thus "brother's name is John" is a lie.

 

[frigidweirdo]

If he has no brother, then his brother's name is not John. Thus "brother's name is John" is a lie.

But doesn't mean he doesn't have a brother.

Doesn't mean anything.

I could lie and say my brother's name is John, when I have a brother.
I could like and say my brother's name is John when I don't have a brother.

He's not saying he has a brother. Therefore we can't conclude anything. He could have a brother of he could not have a brother.

 

[MinTrut]

So, it doesn't actually fit the definition - whatever that may be - of a maths puzzle?

Well, it's kind of a mess, hence all the ensuing discussions, but it's a math thing, not a logic thing.

 

[MinTrut]

Depends what you mean by "always lies".
If you say "My brother's name is John", where is the lie? Or is all of it a lie?

He didn't say he has or doesn't have a brother. So he's not lying.
Therefore when saying "all of my hats are green", doesn't mean he has hats, or that he doesn't have hats. We can't conclude anything from that at all.

All we can conclude is that whatever hats he may have, one isn't green. Nothing more.

Well, from a logical standpoint, the problems and solutions are infinite.

But the attempt of the original was to (poorly) demonstrate a principle in math.

 

[MinTrut]

My Answer. I would have to add option F --> none of the above at the bottom of the list.

To explain why I believe that the narrator's explanation is incorrect: "All my hats are green" is not a conditional statement so "vacuously true" does not apply. Let say I'm Pinocchio. In order for all my hats to be green, I must have hats. The hats must exist for the statement to be true. A nonexistent hat cannot have the attribute of being green (zero hats). Thus answer C is possibly correct; however, we cannot conclude that answer C ( 0 hats) is the correct answer unless that is the only way the statement can be a lie. Since answer A (at least one hat) is also possibly if there is a non-green hat, we cannot conclude either A or C alone. Talso, the other answers are incorrect for the reasons stated in the video.

Had Pinocchio said "If I have hats, then all my hats are green" , then "vacuously true" would apply since the premise of "I have hats" was not met to begin with, so there is no determination of the conclusion "All my hats are green" if there are no hats. The statement "All my hats are green" does not establish a premise of a conditional statement, so "vacuously true" does not apply. Notice the example of "All the mobile phones in the room are turned off" also does not establish a premise of a conditional statement, so "vacuously true" does not apply to that statement either. A mobile phone must exist to have the state of being either turned on or turned off. Zero mobile phones cannot be in the state of turned on or turned off because there is no phone.

And one more thing, being a math ol

Yeah - from a logical standpoint, F makes the most sense, and was my answer before I learned this was a math problem.

But from a math standpoint, it's a different problem.

 

[MinTrut]

But doesn't mean he doesn't have a brother.

Doesn't mean anything.

I could lie and say my brother's name is John, when I have a brother.
I could like and say my brother's name is John when I don't have a brother.

He's not saying he has a brother. Therefore we can't conclude anything. He could have a brother of he could not have a brother.

You're being logical, but this problem exists within a different and more limited spectrum.

 

[JoeMoma]

But doesn't mean he doesn't have a brother.

Doesn't mean anything.

I could lie and say my brother's name is John, when I have a brother.
I could like and say my brother's name is John when I don't have a brother.

He's not saying he has a brother. Therefore we can't conclude anything. He could have a brother of he could not have a brother.

Exactly! That is why neither answer A nor answer C can be concluded independently from the logic puzzle.

 

[JoeMoma]

Yeah - from a logical standpoint, F makes the most sense, and was my answer before I learned this was a math problem.

But from a math standpoint, it's a different problem.

The math used in the youtube video did not properly model the logic puzzle. I could look at the problem and say 1 +1 = 2 which is mathematically true but that doesn't properly model the logic puzzle either.

 

[MinTrut]

The math used in the youtube video did not properly model the logic puzzle. I could look at the problem and say 1 +1 = 2 which is mathematically true but that doesn't properly model the logic puzzle either.

It's not a logic puzzle, it's a math puzzle - that's explained right away in the video.

A logic puzzle would permit a staggering range of alternate answers, but not this math puzzle.

 

[JoeMoma]

It's not a logic puzzle, it's a math puzzle - that's explained right away in the video.

A logic puzzle would permit a staggering range of alternate answers, but not this math puzzle.

It's both a logic puzzle and a math puzzle. Thus, to get a correct answer the puzzle, the boolean algebra has to correctly model the written statements of the puzzle.

 

[MinTrut]

It's both a logic puzzle and a math puzzle. Thus, to get a correct answer the puzzle, the boolean algebra has to correctly model the written statements of the puzzle.

It's really barely a puzzle at all, and should never have been called anything other than a math knowledge question.

All the logic stuff can (and has for many) act (acted) as a distraction from what's really being asked, which is whether the test taker knows their math rules.