Interesting Problem *Warning Intellectual Content*

[310Rduner]

Four cards are presented: E, C, 4, and 5. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? "If a card has a vowel on one side, then it has an even number on the other side."

Answers to follow after people get their chance to answer.

[Taco]

E

[Big400EX]

Originally posted by Taco
E

What he said.:p

[batgeek]

this better be some kinda new drinking game. :cool:

[kamikaze_rzrbak]

5

[ewalker302]

All of them

[kwatts400]

All of them.

[Tommy 17]

no VOWEL is a even number... they are all odds...


so don't even waste ur time turning over cards:o

[wilkin250r]

The "E" and the "5"

[Rip_Tear]

Just the E.

It doesn't say anything about if a card has an odd number then it has a vowel on it...

[wilkin250r]

We agree on the "E", because it is a vowel, and we need to verify that it has an even number on the other side.

But also, we need to see the other side of the "5" to make sure it DOESN'T have a vowel on the other side.;)

[modracer5]

e and 4

[member]

dang just turn em all over and find out

[trick450r]

im going with tommyt none of em...

[theTman]

E...or is it C ???????

[K_Banger125]

all:confused:

[ewalker302]

Ok 310, so what's the answer???

I still say all of them, because all but any one of them could be right, and any one of them could be wrong.

:bandit:

[310Rduner]

Originally posted by ewalker302
Ok 310, so what's the answer???

I still say all of them, because all but any one of them could be right, and any one of them could be wrong.

:bandit:

Wilkin would be "teh correct". E and 5.

The reason for this has to do with the rules of conditional statements. The task is not to Confirm the statement, but to prove it false. It is in the order of if A then B. The same rules do not apply in the order of if B then A.
There is no point in flipping over the 4 card. There is no rule here saying that the 4 card cannot have either a vowel or a consonant. However if you turn over the 5 card and find a vowel then you have proven the statement false. The same way you approach statements in math basically. You do not check statements to see more cases when they are correct, you are looking for a single case that it is wrong.

Here is another analogy to better understand it.

Let the cards show "beer," "cola," "16 years," and "22 years." On one side of each card is the name of a drink; on the other side is the age of the drinker. What card(s) must be turned over to determine if the following statement is false? If a person is drinking beer, then the person is over 19-years-old.

Obviously you would not flip over the cola, or 22 cards as those instances do not prove it false. There is no rule saying a 22 year old can't drink a cola. However, you flip over the beer and 16 card because those would prove the statement as false if the person were under 19 and drinking a beer.

[seatec]

HIJACK!!

A man is lying dead in a field and next to him is a package. had he opened the package he would still be alive!
What's in the package?

[mikeminyard]

A parachute.

[MY450R]

triple fudge sunday

[seatec]

YOu are not allowed to play anymore. lol

[Blysster]

life savers?

[wilkin250r]

Of course I had it correct. Why would anybody doubt me?

[Tommy 17]

Originally posted by wilkin250r
Of course I had it correct. Why would anybody doubt me?


yeah well:blah:

[ewalker302]

Originally posted by 310Rduner
Four cards are presented: E, C, 4, and 5. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? "If a card has a vowel on one side, then it has an even number on the other side."



If E has an even # on the other side and 5 has a consonant on the other side, but 4 has a consonant then it takes three cards to prove the statement false.

If E has an even # on the other side and 5 has a consonant on the other side, and 4 has a vowel, but C has an even # on the other side it takes all 4 to prove the statement false.

The analogy you give is not relevant, there are no limiting factors like the legal age to drink in the original problem.

I don't understand why you say there is no reason to turn over the four card, the statement is " If a card has a vowel on one side, then it has an even # on the other side". So if it has anything other than a vowel on the other side, the statement is false.
There were no conditions stated in the problem, other than a card with a # on one side has a letter on the other and vice versa.



:bandit:

[310Rduner]

Originally posted by ewalker302
If E has an even # on the other side and 5 has a consonant on the other side, but 4 has a consonant then it takes three cards to prove the statement false.

If E has an even # on the other side and 5 has a consonant on the other side, and 4 has a vowel, but C has an even # on the other side it takes all 4 to prove the statement false.

The analogy you give is not relevant, there are no limiting factors like the legal age to drink in the original problem.

I don't understand why you say there is no reason to turn over the four card, the statement is " If a card has a vowel on one side, then it has an even # on the other side". So if it has anything other than a vowel on the other side, the statement is false.
There were no conditions stated in the problem, other than a card with a # on one side has a letter on the other and vice versa.



:bandit:

Here is a full explanation of why you are completely wrong, and incredibly off base.


"I gave the Wason Card Problem to 100 students last semester and only seven got it right, which was about what was expected. There are various explanations for these results. One of the more common explanations is in terms of confirmation bias. This explanation is based on the fact that the majority of people think you must turn over cards A and 4, the vowel card and the even-number card. It is thought that those who would turn over these cards are thinking "I must turn over A to see if there is an even number on the other side and I must turn over the 4 to see if there is a vowel on the other side." Such thinking supposedly indicates that one is trying to confirm the statement If a card has a vowel on one side, then it has an even number on the other side. Presumably, one is thinking that if the statement cannot be confirmed, it must be false. This explanation then leads to the question: Why do most people try to confirm a statement, when the task is to determine if it is false? One explanation is that people tend to try to fit individual cases into patterns or rules. The problem with this explanation is that in this case we are instructed to find cases that don't fit the rule. Is there some sort of inherent resistance to such an activity? Are we so driven to fit individual cases to a rule that we can't even follow a simple instruction to find cases that don't fit the rule? Or, are we so driven that we tend to think that the best way to determine whether an instance does not fit a rule is to try to confirm it and if it can't be confirmed then, and only then, do we consider that the rule might be wrong?

Corey noted that when the problem is changed from abstract items, such as numbers and letters, and put in concrete terms, such as drinks and the age of the drinker, the success rate significantly increases (see the example described above). One would think that confirmation bias would lead most people to say they must turn over the beer card and the 22 card, but they don't. Most people see that the cola and 22 cards are irrelevant to solving the problem. If I remember correctly, Corey explained the difference in performance between the abstract and concrete versions of the problem in terms of evolutionary psychology: Humans are hardwired to solve practical, concrete problems, not abstract ones. To support his point, he says he simplified the abstract test to include only two cards (showing 1 and 2) with equally poor results.

I had discussed confirmation bias, but not conditional statements, with my classes before giving them the Wason problem. The majority seemed to understand confirmation bias; so, if the reason so many do so poorly on this problem is confirmation bias, then just knowing about confirmation bias is not much help in overcoming it as a hindrance to critical thinking. This is consistent with what I teach. Recognition of a hindrance is a necessary but not a sufficient condition for overcoming that hindrance. However, next semester I'm going to give my students the Wason test after I discuss determining the truth-value of conditional statements. The reason for doing so is that anyone who has studied the logic of conditional statements should know that a conditional statement is false if and only if the antecedent is true and the consequent is false. (The antecedent is the if statement; the consequent is the then statement.) So, the statement If a card has a vowel on one side, then it has an even number on the other side can only be false if the statement a card has a vowel on one side is true and the statement it has an even number on the other side is false. I must look at the card with the vowel showing to find out what is on the other side because it could be an odd number and thus would show me that the statement is false. I must also look at the card with the odd number to find out what is on the other side because it could be a vowel and thus would show me that the statement is false. I don't need to look at the card with the consonant because the statement I am testing has nothing to do with consonants. Nor do I need to look at the card with the even number showing because whether the other side has a vowel or a consonant will not help me determine whether the statement is false.

There is a possibility that the reason many think that the even-numbered card must be turned over is that they mistakenly think that the statement they are testing implies that if a card has an even number on one side then it cannot have a consonant on the other. In other words, it is possible that the high error rate is due to misunderstanding logical implication rather than confirmation bias. In the concrete version of the problem, perhaps it is much easier to see that the statement If a person is drinking beer, then the person is over 19-years-old does not imply that if a person is over 19 then they cannot be drinking cola. If this is the case, then an explanation in terms of the difference between contextual implication and logical implication might be better than one in terms of confirmation bias. Perhaps it is the context of drinking and age of the drinker that indicates to many people that a person can be over 19 and not drink beer without falsifying the statement being tested, i.e., that simply because if you're drinking beer you are over 19 doesn't imply that if you're over 19 you can't be drinking cola. That is, in the concrete case people may not have any better understanding of logical implication than they do in the abstract case and neither case may have anything to do with confirmation bias.

On the other hand, some might reason that if I turn over the even card and find a vowel, then I have confirmed the statement, which is in effect the same as showing that the statement is not false, but true. This would be classic confirmation bias. Finding an instance that confirms the rule does not prove the rule is true. But, finding one instance that disproves the rule shows that the rule is false."