Results 1 to 5 of 5

Math Help - Elements

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    12

    Elements

    There are 3 sets A, B and C, such that B is a proper subset of A (BcA),intersection of A and B #0, intersection of C and B #0, whereby
    n(U) = 95. There are altogether 22 elements in the intersection of the complements of these three sets. Set B contains 31 elements whereas the intersection of A and C has 34 elements. The number of elements in A and C but not in B is one more than half the number in A and C. The number of elements in C, not in A and not in B is 4 more than the number of elements in A, not in C and not in B.
    Work out the numbers in the various regions and state them on the Venn diagram that depicts the relationship of A, B and C as given above.

    pls help me solve this.
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello liptonpc

    Welcome to Math Help Forum!
    Quote Originally Posted by liptonpc View Post
    There are 3 sets A, B and C, such that B is a proper subset of A (BcA),intersection of A and B #0, intersection of C and B #0, whereby
    n(U) = 95.
    Look at the attached diagram.
    There are altogether 22 elements in the intersection of the complements of these three sets.
    This statement gives us the 22 outside the three set loops.
    Set B contains 31 elements whereas the intersection of A and C has 34 elements.
    Initially I wrote x in the intersection of B and C (where the 16 is now), and therefore (31 - x) in the area representing B \cap C' (where the 15 is) and 34-x in A\cap C\cap B' (where the 18 is).
    The number of elements in A and C but not in B is one more than half the number in A and C.
    This is potentially ambiguous. What does "The number of elements in A and C but not in B" mean? I am assuming it means "The number of elements that are in A and in C but not in B"; in other words the number of elements in A \cap C \cap B'. And I'm also assuming that "the number in A and C" means the number that are in A and in C; in other words the number in A \cap C, which (we've been told) is 34. So:
    n(A \cap C \cap B') = \tfrac12\times34+1 = 18
    So this gives us x = 34-18 = 16, and the 15 in B\cap C'.
    The number of elements in C, not in A and not in B is 4 more than the number of elements in A, not in C and not in B.
    Initially I wrote y in A\cap B' \cap C' (where the 10 is now); and therefore I wrote y+4 in C\cap A' (where the 14 is). So I was then able to total up the numbers, and put the result equal to 95. This gave:
    y + 31 + 18 + y+4+22 = 95

    \Rightarrow 2y + 75=95

    \Rightarrow y = 10
    So those are my answers, which I believe to be correct based on the assumption that I have interpreted the phrase "the number in A and C but not in B" correctly.

    Grandad
    Attached Thumbnails Attached Thumbnails Elements-untitled.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    12
    Hi Grandad,
    i have something dont understand.

    There are altogether 22 elements in the intersection of the complements of these three sets.
    I think this statement "A∩B∩C =22" gives us the 22 inside the three set?

    and
    The number of elements in A and C but not in B is one more than half the number in A and C.
    one more than half <-- is it mean 1 1/2 (1.5) ??

    i have att exercise.
    thanks for reply.
    Lipton
    Attached Thumbnails Attached Thumbnails Elements-1.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello liptonpc
    There are altogether 22 elements in the intersection of the complements of these three sets.
    This is n(A'\cap B'\cap C') - not n(A\cap B\cap C).

    The number of elements in A and C but not in B is one more than half the number in A and C.

    one more than half <-- is it mean 1 1/2 (1.5) ??
    No: this would be "one-and-a-half times as many".

    "One more than half of" x is \tfrac12x+1.

    1.5x is "one-and-a-half times as many" as x, or "half as many again" as x.

    English can be very confusing sometimes, can't it?

    Grandad
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    12
    yeah ^^ got it ^^ thanks Grandad ^^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 10th 2011, 07:40 PM
  2. Replies: 8
    Last Post: November 27th 2011, 11:18 PM
  3. [SOLVED] Why are these not elements of W
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: October 22nd 2011, 04:02 PM
  4. Elements
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: December 9th 2008, 05:52 PM
  5. elements of a set
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 3rd 2008, 02:57 AM

Search Tags


/mathhelpforum @mathhelpforum