Results 1 to 4 of 4

Math Help - need help!!!

  1. #1
    Member
    Joined
    Oct 2006
    Posts
    184
    Thanks
    1

    need help!!!

    If we have two sets, A and B, contained in the universal set
    Can someone tell me why the smallest possible number of elements of
    (A intersect B) occurs when A union B = universal set???

    i know that
    n(A intersect B) = n(A) + n(B) - n(A union B)
    so to make it smaller, we need to make n(A union B) as big as possible.

    But is there a way to explain this without using the formula above???
    Last edited by acc100jt; October 28th 2006 at 01:06 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by acc100jt View Post
    If we have two sets, A and B, contained in the universal set
    Can someone tell me why the smallest possible number of elements of
    (A intersect B) occurs when A union B = universal set???

    i know that
    n(A intersect B) = n(A) + n(B) - n(A union B)
    so to make it smaller, we need to make n(A union B) as big as possible.

    But is there a way to explain this without using the formula above???
    I'm not sure I understand the question. for instance let D={0,1,2,3,4} be
    our universe of discourse (universal set), and let A={0,1}, B={2,3}, then
    |A Intersect B|=0, but A Union B != D.

    Similarly let A={0,1,2}, B={2,3,4}, then |A Intersect B|=1, and A Union B =D.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2006
    Posts
    184
    Thanks
    1
    sorry, let me restate my questions,

    If the sets A and B are not disjoint.
    n(universal set)=60
    n(A)=32
    n(B)=34
    then the least n(A intersect B) occurs when (A union B)=universal set.
    WHY??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by acc100jt View Post
    sorry, let me restate my questions,

    If the sets A and B are not disjoint.
    n(universal set)=60
    n(A)=32
    n(B)=34
    then the least n(A intersect B) occurs when (A union B)=universal set.
    WHY??
    Because n(A)+n(B)>n(U), there must be some elements shared between
    A and B. The smallest number that could be shared is 6 (that is:
    n(A)+n(B)-n(U), any smaller number of shared elements will leave n(A Union
    B)>60, which would be a contradiction).

    But if A and B share exactly 6 elements then n(A Union B)=60, and so
    A Union B=U.

    RonL

    RonL
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum