Results 1 to 9 of 9

Math Help - Set Theory

  1. #1
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155

    Set Theory

    In a certain city, one-seventh of the population who are left-handed are also short-sighted, and two-ninths who are short-sighted are also left-handed.
    One twelfth are neither left-handed nor short-sighted.
    Given that the number of people who are left-handed and short-sighted is 2x, draw a Venn diagram to illustrate this information.
    (The Venn diagram should show the number of elements, in terms of x, in each area.)

    \color{red}\text{Find the fraction of the population who are}
    \color{red}\text{a)left-handed but not short-sighted,}
    \color{red}\text{b)either left-handed or short-sighted, but not both.}
    \color{red}\text{If there are 154000 people who are left-handed, find the total population.}
    Last edited by SengNee; January 14th 2008 at 11:46 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by SengNee View Post
    In a certain city, one-seventh of the population who are left-handed are also short-sighted, and two-ninths who are short-sighted are also left-handed.

    One twelfth are neither left-handed nor short-sighted. Mr F asks: 1/12 of what? The total population?

    Given that the number of people who are left-handed and short-sighted is 2x, draw a Venn diagram to illustrate this information.
    (The Venn diagram should show the number of elements, in terms of x, in each area.)

    Find the fraction of the population who are
    a)left-handed but not short-sighted,
    b)either left-handed or short-sighted, but not both.
    If there are 154000 people who are left-handed, find the total population.
    Attached is what the Venn diagram looks like.

    From the given info: (a + 2x)/7 = 2x => a = 12x.

    2(2x + b)/9 = a + 2x = 14x => b = 61x.

    c = (a + 2x + b + c)/12 = (75x + c)/12 => c = 75x/11.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155
    Quote Originally Posted by mr fantastic View Post
    Attached is what the Venn diagram looks like.

    From the given info: (a + 2x)/7 = 2x => a = 12x.

    2(2x + b)/9 = a + 2x = 14x => b = 61x.

    c = (a + 2x + b + c)/12 = (75x + c)/12 => c = 75x/11.
    I think you are wrong.


    L=Left-handed
    S=Short-sighted

    White=Right-handed and Not short-sighted
    Red= Left-handed and Not short-sighted
    Purple=Left-handed and Short-sighted
    Blue=Right-handed and Short-sighted


    Are you agree??
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by SengNee View Post
    I think you are wrong.


    L=Left-handed
    S=Short-sighted

    White=Right-handed and Not short-sighted
    Red= Left-handed and Not short-sighted
    Purple=Left-handed and Short-sighted
    Blue=Right-handed and Short-sighted


    Are you agree??
    So where do you think my Venn diagram is wrong? On your one, isn't purple the intersection of the red and blue .....? That doesn't make sense to me.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155
    Quote Originally Posted by mr fantastic View Post
    So where do you think my Venn diagram is wrong? On your one, isn't purple the intersection of the red and blue .....? That doesn't make sense to me.
    I see, pardon me.

    Can you answer the question completely?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by SengNee View Post
    I see, pardon me.

    Can you answer the question completely?
    Well, I've already given you the Venn diagram and found in terms of x the number of elements in each subset. Where are you stuck?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155
    Quote Originally Posted by mr fantastic View Post
    Well, I've already given you the Venn diagram and found in terms of x the number of elements in each subset. Where are you stuck?
    The red part.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by SengNee View Post
    The red part.
    All of the questions ....??
    Quote Originally Posted by SengNee View Post
    In a certain city, one-seventh of the population who are left-handed are also short-sighted, and two-ninths who are short-sighted are also left-handed.
    One twelfth are neither left-handed nor short-sighted.
    Given that the number of people who are left-handed and short-sighted is 2x, draw a Venn diagram to illustrate this information.
    (The Venn diagram should show the number of elements, in terms of x, in each area.)

    \color{red}\text{Find the fraction of the population who are}
    \color{red}\text{a)left-handed but not short-sighted,}
    \color{red}\text{b)either left-handed or short-sighted, but not both.}
    \color{red}\text{If there are 154000 people who are left-handed, find the total population.}
    If everything got answered, there'd be nothing left for you to do ..... What have you tried?

    The total population is P = a + 2x + b + c = ......

    1) According to the Venn diagram, how many are left handed but not short-sighted? Divide that by P. There's the answer.

    2) According to the Venn diagram, how many are left handed or short-sighted but not both? Divide that by P. There's the answer.

    3) According to the Venn diagram, how many are left handed? Equate that to 154000 and solve for x. Sub x into P. There's the answer.

    Please be specific on exactly where you're stuck.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155
    Quote Originally Posted by mr fantastic View Post
    All of the questions ....??

    If everything got answered, there'd be nothing left for you to do ..... What have you tried?

    The total population is P = a + 2x + b + c = ......

    1) According to the Venn diagram, how many are left handed but not short-sighted? Divide that by P. There's the answer.

    2) According to the Venn diagram, how many are left handed or short-sighted but not both? Divide that by P. There's the answer.

    3) According to the Venn diagram, how many are left handed? Equate that to 154000 and solve for x. Sub x into P. There's the answer.

    Please be specific on exactly where you're stuck.

    Show me the answer please.
    Don't worry about that nothing is left for me to try, I can find other similar exercises to try.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 06:09 PM
  2. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  3. Problems relating Theory of Automata (Computer Theory)
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: October 17th 2007, 09:52 AM
  4. Set theORY
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2007, 07:01 PM
  5. Set Theory
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 27th 2007, 09:22 AM

Search Tags


/mathhelpforum @mathhelpforum