# Thread: [SOLVED] A logic question

1. ## [SOLVED] A logic question

Hi,

We were discussing about a logic question with my friends. And we haven't agreed the right answer.
I want to ask this question to you. If you answer we will be happy.
Sorry for bad English.
Thank you.

These are the rules:

• You will be given a hyphothesis to be examined on.
• You will be shown some cards. One side of the card is a letter and other side of the card is number.
• You are going to see only one side of the card.
• And you are going to decide if you switch(to look or check) or not the other side of the card to examine the hyphothesis.

Hyphothesis: If one side of a card is letter 'D', other side of the card has to be number '7'.

You see these cards: 7, A, 8, 9, D, G

Which cards are you going to switch to examine the hyphothesis?

2. Hint: If $\displaystyle D$ then $\displaystyle 7$ is the same as $\displaystyle D$ only if $\displaystyle 7$.

3. My solution is like this:

I am going to switch the D to check if the other side is 7. If it is 7 no problem. But if it is not 7 the hyphothesis fails.

I won't switch 'A'. Because there will be no problem is the number is 7 or not. This won't prove the hyphothesis is true or not.

I will switch 8. Because if the other side of the card is D the hyphothesis will fail. If not no problem.

9 as well, same as above.

I won't switch card G. Same reason as the card A.

I am not sure if i have to switch card 7.
The hyphothesis do not tell me if one side of the card is 7 other side has to be D. From this point of view, i won't switch.

But there is two side of a card and hyphothesis tell me if one side is D other side will be 7. Is this mean: if one side is 7 other side has to be D.

I am stuck this point.

4. Originally Posted by mkahraman
I am not sure if i have to switch card 7.
The hyphothesis do not tell me if one side of the card is 7 other side has to be D. From this point of view, i won't switch.
There is no need to test card $\displaystyle 7$.
Even if there is a non $\displaystyle D$ on the other side it changes nothing.

5. Yeah, thank you now i am clear.

I will switch these cards: All numbers that is not 7 and only the letter 'D'

Am i right?

If someone thinks different than me or same as me please post this subject so that i can show my friends the right answer.

6. Originally Posted by mkahraman
Yeah, thank you now i am clear.
I will switch these cards: All numbers that is not 7 and only the letter 'D'
Am i right?
You are correct.
If each 'letter' side had a '7' on the other side the orginial statement is still true.

7. I'm puzzled. Did you miss a "not" out in your first post. There is nothing to prevent a card with a 7 on one side having anything else at all on the other side even if the hypothesis is true, as I can see you are well aware from your other posts (and would not have doubted for one moment).
"If d then 7" is the same as "if not 7 then not d" , but not the same as "7 only if d".

8. These three statements are equivalent.
If D then 7.
D only if 7.
If not 7 then not D.

9. I'm sorry Plato, but I stand by what I said.
Elementary text books somtimes even define p=>q by "not(p and not q)", so I think the first of my statements is surely correct.
So it seems you must still think that "if d then 7" is the same as "7 only if d". If you had put "only 7 if d" then I would agree with you, but for me "7 only if d" means something quite different, it would mean that a 7 could only appear on a card with a d on the other side, but we both know that is not the case. I think my interpretation of what you wrote is the natural one, so that your second post is confusing at best.
Since you think I am ignorant, perhaps you could enlighten me if I am mistaken.

10. Originally Posted by mkahraman

I will switch these cards: All numbers that is not 7 and only the letter 'D'

Thank you friends. I found a document about this question. According to the paper 10% of the people gave the correct answer for this question.
Be carefull the example is differs with the one i wrote above.

So the quoted answer is the correct one.

http://www.emis.de/proceedings/PME28...050_Inglis.pdf