Results 1 to 7 of 7

Math Help - Cardinality of these sets!

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    8

    Cool Cardinality of these sets!

    Hey guys, this is my first post, was just wondering if i could get your help. I'm studying for my repeats and you guys can save me.

    If X = {1,2,3,4}, Y = {2,4,6} what is the cardinality of the following sets?

    (i) A = {x|x mod 2 = 0 and 0 <=x<=20}
    (ii) B = X * X * Y
    (iii) C = {(x,y)|x ≠ y and x,y ∈ X}

    Please explain your train of thought in solving this. I am trying hard to understand the right way to approach this question quickly, Thank you for your time guys...
    Last edited by Aeonitis; August 4th 2010 at 08:28 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2010
    Posts
    8
    I've tried them out, with the following answers:-

    (i) A = {2,4,6,8,10,12,14,16,18,20}, Therefore A has a cardinality of 10 (elements).
    (ii) B = Cartesian Product of 'X times X times Y' or better yet '4 by 4 by 3' elements each to give a total of 48 in cardinality?!
    (iii) C = UNSOLVED!!!

    I wanna make sure someone agrees with me having the right answers since you're the pros

    I really wanna know what the '|' symbol stands for or means, as in 'x|x'. Hard to specifically search for in a book.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,961
    Thanks
    1784
    Awards
    1
    Quote Originally Posted by Aeonitis View Post
    I've tried them out, with the following answers:-
    (i) A = {2,4,6,8,10,12,14,16,18,20}, Therefore A has a cardinality of 10 (elements).
    (ii) B = Cartesian Product of 'X times X times Y' or better yet '4 by 4 by 3' elements each to give a total of 48 in cardinality?!
    (iii) C = UNSOLVED!!!
    I really wanna know what the '|' symbol stands for or means, as in 'x|x'. Hard to specifically search for in a book.
    Parts a & b are correct.
    For part c: |X\times X|-|X|=16-4=12.

    For integers x|y usually means x divides y.
    But it can mean other things.
    What is the context of you question?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2010
    Posts
    8
    Quote Originally Posted by Plato View Post
    For part c: |X\times X|-|X|=16-4=12.

    For integers x|y usually means x divides y.
    But it can mean other things.
    What is the context of your question?
    I guess there's a chance that De Morgan's Law might plays a part in this since before this question, i was asked to write down De Morgan's Laws for sets. Found a way to type the symbols accurately, To put it precisely, the 'C' question is

    C = {(x,y)|x ≠ y and x,y ∈ X}

    I do know that '/' means divide, but i'm assuming that the symbol '|' plays a different part, am I wrong?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,961
    Thanks
    1784
    Awards
    1
    Quote Originally Posted by Aeonitis View Post
    C = {(x,y)|x ≠ y and x,y ∈ X}
    I do know that '/' means divide, but i'm assuming that the symbol '|' plays a different part, am I wrong?
    In that context the “|” is read as “such that”: The set of ordered pairs (x,y) such that x is not y and…”
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,416
    Thanks
    1853
    "x/y" means the number "x divided by y" but it is more common to use "|" for the statement "x|y" meaning "x divides evenly into y (has remainder 0)".

    Here, however, it is clear (to me, anyway) that the "|" is just separating the pairs (x,y) from the condition " x\ne y". This set is the set of all pairs (x, y) from X (so x and y can be any of 1, 2, 3, 4) such that x is not equal to y.

    X itself has 4 members so X\times X has 16 members. Requiring that x\ne y drops 4 of those: (1, 1), (2, 2), (3, 3), and (4, 4). X contains 16- 4= 12 members.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2010
    Posts
    8
    Thank you guys, i will post the full answer for future questioneers

    (i) A = {2,4,6,8,10,12,14,16,18,20}, Therefore A has a cardinality of 10 (elements).
    (ii) B = Cartesian Product of 'X times X times Y' or better yet '4 by 4 by 3' elements each to give a total of 48 in cardinality?!

    (iii) C = {(x,y)|x ≠ y and x,y ∈ X}

    pairs x,y {such as (1,1),(1,2),etc...} drawn from set X with a cardinality of '4 by 4 = 16' as in the question "x,y ∈ X". Due to the statement 'x ≠ y' pairs can't come in equals, discarding the following four sets (1,1),(2,2),(3,3),(4,4). The end product is 16-4 giving a cardinality of 12 for set 'C'.

    Thank you so much Guys
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Cardinality of Sets and Power Sets
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 8th 2011, 06:26 PM
  2. cardinality of sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 7th 2010, 01:42 PM
  3. Cardinality of Sets
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: May 3rd 2010, 10:09 AM
  4. Cardinality of sets Q and R
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 14th 2009, 01:30 PM
  5. Cardinality of sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 18th 2007, 04:30 PM

Search Tags


/mathhelpforum @mathhelpforum