Results 1 to 2 of 2

Math Help - simple set example

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    CZ
    Posts
    1

    Question simple set example

    I can't figure out why the correct anwer is a)

    Each of 35 students learns at least one of these languages: English, German, French.
    5 students study all of these languages.
    20 students study English.
    15 students study German
    10 students study French.


    Decide which of these statement is true:


    a) No student exists, who learns exactly 2 languages.
    b) At least one student learns exactly 2 languages.
    c) At least one student learns French and German and doesn't learn English.
    d) Described situation cannot happen.
    d) None of the statements is correct.


    I would greatly appreciate if you describe how you got the result.
    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,561
    Thanks
    785

    Re: simple set example

    Let x, y and z denote (in some order) the number of students who study exactly two languages. Then by the inclusion–exclusion principle, we have

    20 + 15 + 10 - (x + 5) - (y + 5) - (z + 5) + 5 = 35

    from where x + y + z = 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 2nd 2012, 09:05 AM
  2. simple interest and simple discount
    Posted in the Business Math Forum
    Replies: 1
    Last Post: July 21st 2012, 08:37 PM
  3. [SOLVED] Really simple question too hard for a simple mind
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 5th 2010, 09:03 AM
  4. Easy Question - Simple Interest, Simple Discount
    Posted in the Business Math Forum
    Replies: 0
    Last Post: September 21st 2010, 09:22 PM
  5. Replies: 4
    Last Post: May 4th 2010, 10:08 AM

Search Tags


/mathhelpforum @mathhelpforum