Results 1 to 10 of 10

Math Help - [SOLVED] A logic question

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    6

    [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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1
    Hint: If D then 7 is the same as D only if 7.
    Last edited by Plato; November 12th 2009 at 02:38 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    6
    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by mkahraman View Post
    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 7.
    Even if there is a non D on the other side it changes nothing.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    6
    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.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by mkahraman View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member alunw's Avatar
    Joined
    May 2009
    Posts
    188
    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".
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1
    These three statements are equivalent.
    If D then 7.
    D only if 7.
    If not 7 then not D.
    Last edited by Plato; November 12th 2009 at 02:36 AM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member alunw's Avatar
    Joined
    May 2009
    Posts
    188
    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.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Nov 2009
    Posts
    6
    Quote Originally Posted by mkahraman View Post

    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Logic check, and mini question.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 11th 2009, 01:25 PM
  2. [SOLVED] Logic Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 29th 2009, 08:11 PM
  3. [SOLVED] logic sets
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: February 3rd 2009, 08:35 AM
  4. [SOLVED] logic question
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 15th 2008, 07:49 PM
  5. [SOLVED] predicate logic HELP!
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: June 21st 2007, 10:46 AM

Search Tags


/mathhelpforum @mathhelpforum