Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem Involving Counting of Elements in Three Sets

  1. Oct 9, 2012 #1
    Problem:
    -The Union of set A, set B and set C has 104 elements.
    -The Union of Set A and B has 51 elements
    -The Union of Set A and C has 84 elements
    -The Union of Set B and C has 97 elements
    -The Intersection of Set A and the Union of Set B and C has 17 elements.
    -Set C has twice as many elements as set B and three times as many elements as Set A.

    How many elements does A have?

    Hint: Take C is 6x and solve for x.

    This is what I did after drawing a Venn diagram:

    A minus B[itex]\cup[/itex]C = 104-97=7
    B minus A[itex]\cup[/itex]C = 104-84=20
    C minus A[itex]\cup[/itex]B = 104-51=53

    If you add up these numbers and subtract them from 104, you'll get that all the intersections of these sets together have 24 elements.

    It is given that A[itex]\cap[/itex](B[itex]\cup[/itex]C) = 17.

    Therefore, the intersection of B and C without whatever is in A, should be 7.

    From this fact the elements of A can be calculated from the fact that A[itex]\cup[/itex]C has 84 elements. To calculate the elements of A take 84 and subtract the elements of C that are not in A, 84 -53 -7= 24

    I didn't use the hint nor did I use the size relationship between the sets, so I am not sure if I did this problem right.

    How could I solve this problem with the hint (solve as an equation of x) and the given relationship between A, B and C?
     
    Last edited: Oct 9, 2012
  2. jcsd
  3. Oct 9, 2012 #2
    Huh?
     
  4. Oct 9, 2012 #3
    Sorry, typo.

    Set C is twice as large as B and three times as large as A.
     
  5. Oct 9, 2012 #4
    You only need to use three of the above 7 conditions to determine the size of A, so hopefully there are some interesting follow-up questions to your problem. Given that unhelpful hint, that does not seem too likely.
     
  6. Oct 9, 2012 #5
    The hint and the size relationship confused me. I don't see how to solve this problem as an equation of x and given the fact that C is twice as large as B and three times as A, but I guess it is possible. If someone sees it, I am curious how to proceed.

    There is no follow up question to this problem.

    The teacher of this course is a little bit nuts though, on another test he asked to prove that every even integer greater than 4 can be written as the sum of two primes for extra credit.
     
    Last edited: Oct 9, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem Involving Counting of Elements in Three Sets
  1. Counting Problems (Replies: 2)

Loading...