The cards are on the table

[Speakpigeon]

Eight cards are on the table.

Each card has one capital letter (e.g. F, G, X etc.) on one side, and one number (below 10, e.g. 3, 7, 8 etc.) on the other side.

At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.

What are the cards you really need to turn over to determine whether or not it's true of all the cards on the table that if there is a vowel on one side, then there is an even number on the other side.

There is no trick. I'm just asking to have your opinion.

Take your time and don't let other people's answers sway your best judgement... You could live to regret it!
EB

 

[PyramidHead]

if there is a vowel on one side, then there is an even number on the other side.

Is this "if" an "if and only if"? In other words, does the hypothesis in question entail that consonants will have only odd numbers on the other side, or could consonants have either even or odd ones?

 

[bilby]

Eight cards are on the table.

Each card has one capital letter (e.g. F, G, X etc.) on one side, and one number (below 10, e.g. 3, 7, 8 etc.) on the other side.

At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.

What are the cards you really need to turn over to determine whether or not it's true of all the cards on the table that if there is a vowel on one side, then there is an even number on the other side.

There is no trick. I'm just asking to have your opinion.

Take your time and don't let other people's answers sway your best judgement... You could live to regret it!
EB

Just the 7 and the 5 - if either has a vowel on the other side, then the claim is false. If there is not, then the claim is true; Although if there are no cards with vowels on them in the set, in which case the claim is still true, the exercise is rather pointless.

That pointless case could be avoided if there were a vowel visible; in that scenario, all cards showing either odd numbers or vowels would need to be checked. Any odd number with a vowel on the back, or any vowel with an odd number on the back, disproves the claim. Cards showing a consonant or an odd number are irrelevant to the claim being tested, and need not be checked.

 

[bigfield]

5 and 7.

The typical form of the puzzle has one card with a vowel face up, and only one card with an odd number face up.

e.g.
https://www.puzzleprime.com/brain-teasers/deduction/vowels-and-even-numbers/

 

[Speakpigeon]

if there is a vowel on one side, then there is an even number on the other side.

Is this "if" an "if and only if"? In other words, does the hypothesis in question entail that consonants will have only odd numbers on the other side, or could consonants have either even or odd ones?

That's your usual "if-then".

Take the whole thing as properly worded and phrased.

If I worded it or phrased it wrong, I won't wrong you for it!
EB

 

[Speakpigeon]

5 and 7.

The typical form of the puzzle has one card with a vowel face up, and only one card with an odd number face up.

"Typical" here is wrong. I understand that the original test had four cards.

e.g.
https://www.puzzleprime.com/brain-teasers/deduction/vowels-and-even-numbers/

Here you have the four cards of the original test but the question is different, as explained in the comment section on the page.

Interesting too, thanks.
EB

- - - Updated - - -

Just the 7 and the 5 - if either has a vowel on the other side, then the claim is false. If there is not, then the claim is true; Although if there are no cards with vowels on them in the set, in which case the claim is still true, the exercise is rather pointless.

That pointless case could be avoided if there were a vowel visible; in that scenario, all cards showing either odd numbers or vowels would need to be checked. Any odd number with a vowel on the back, or any vowel with an odd number on the back, disproves the claim. Cards showing a consonant or an odd number are irrelevant to the claim being tested, and need not be checked.

Thanks for the explanation.
EB

 

[Tom Sawyer]

Just the 5 and the 7. None of the rest of the cards there would factor into the question.

 

[Speakpigeon]

Eight cards are on the table.

Each card has one capital letter (e.g. F, G, X etc.) on one side, and one number (below 10, e.g. 3, 7, 8 etc.) on the other side.

At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.

What are the cards you really need to turn over to determine whether or not it's true of all the cards on the table that if there is a vowel on one side, then there is an even number on the other side.

There is no trick. I'm just asking to have your opinion.

Take your time and don't let other people's answers sway your best judgement... You could live to regret it!
EB

OK, now, suppose no card has a vowel on it, either side.

How do you explain that we say it's true that if there is a vowel on one side, then there is an even number on the other side.
EB

 

[bigfield]

OK, now, suppose no card has a vowel on it, either side.

How do you explain that we say it's true that if there is a vowel on one side, then there is an even number on the other side.
EB

It can't be shown the be true. You could also say that if there is a vowel on one side, then there is an odd number on the other side, but there is no way to determine which of these mutually-exclusive claims is true.