Hint: If then is the same as only if .
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.
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?
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.
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".
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.
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.