Results 1 to 10 of 10

Math Help - Cartesian product.

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    16

    Cartesian product.

    A={a,b,c,d}
    B={y,z}

    A x B = {(a,y),(a,z),(b,y),(b,z),(c,y),(c,z),(d,y),(d,z)}

    B x A = {(y,a),(y,b),(y,c),(y,d),(z,a),(z,b),(z,c),(z,d)}

    I checked the answers and I got A x B wrong but I'm not sure how as I followed the same steps for both.

    Supposedly A x B = {(a,y),(b,y),(c,y),(d,y),(a,z),(b,z),(c,z),(d,z)}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,786
    Thanks
    1683
    Awards
    1
    Quote Originally Posted by Ifailatmaths View Post
    A={a,b,c,d}
    B={y,z}
    A x B = {(a,y),(a,z),(b,y),(b,z),(c,y),(c,z),(d,y),(d,z)}
    B x A = {(y,a),(y,b),(y,c),(y,d),(z,a),(z,b),(z,c),(z,d)}
    I checked the answers and I got A x B wrong but I'm not sure how as I followed the same steps for both.
    Supposedly A x B = {(a,y),(b,y),(c,y),(d,y),(a,z),(b,z),(c,z),(d,z)}
    Those two answers are identical from a set-theory point of view.
    The order in which members are listed makes no difference.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    16
    Quote Originally Posted by Plato View Post
    Those two answers are identical from a set-theory point of view.
    The order in which members are listed makes no difference.
    Even for ordered pairs?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,786
    Thanks
    1683
    Awards
    1
    It is true that in general (a,x)\not=(x,a).

    But it is absolutely true that \{(a,x),(a,y),(b,z)\}=\{(b,z),(a,y),(a,x)\}

    The order in the set makes no difference, only the content of the set.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Feb 2010
    Posts
    466
    Thanks
    4
    Quote Originally Posted by Plato View Post
    It is true that in general (a,x)\not=(x,a).
    You mean it is not in general true that (a,x)=(x,a).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,786
    Thanks
    1683
    Awards
    1
    What is the difference?

    It is true that 1\not= 2.
    It is not true that 1=2.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2008
    Posts
    16
    Quote Originally Posted by Plato View Post
    It is true that in general (a,x)\not=(x,a).

    But it is absolutely true that \{(a,x),(a,y),(b,z)\}=\{(b,z),(a,y),(a,x)\}

    The order in the set makes no difference, only the content of the set.
    Thanks, makes sense.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Feb 2010
    Posts
    466
    Thanks
    4
    Granted that the word 'generally' or 'in general' is sometimes ambiguous, so that it is context that determines what is meant. And in this context, I think you are well enough understood. However, it is more precise to say "it is not in general true that they are equal".

    You say, "It is true in general that they are not equal."

    But it is not true in general that they are not equal, since there are instances in which they ARE equal.

    I say, "It is not in general true that they are equal", which is true since there are instances in which they are NOT equal.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,786
    Thanks
    1683
    Awards
    1
    You must a logician. Only logician would worry with that.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    Feb 2010
    Posts
    466
    Thanks
    4
    Quote Originally Posted by Plato View Post
    You must a logician. Only logician would worry with that.
    Or a neurotic. And I am one. ;-)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cartesian product of A*A*A*A
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 14th 2011, 06:29 AM
  2. Cartesian product
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: August 19th 2011, 11:38 AM
  3. Cartesian product
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 9th 2010, 02:13 AM
  4. Cartesian product
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 26th 2010, 11:30 AM
  5. Cartesian Product
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 9th 2010, 11:31 AM

Search Tags


/mathhelpforum @mathhelpforum