Quandaries and Queries


Name: Susan

Who is asking: Parent
Level: All

My child has the following problems to solve, and we are puzzled.
1. Compare the subset symbols to the inequality symbols of less than or greater than.

2. If A, B & C are sets such that A has 47 elements, B has 32 elements, and C is a proper subset of B, what can you say about the number of elements in the following sets: A U B? A intersect B? B U C? and B intersect C?

Thanks so much!



Hi Susan,

  1. If A is a subset of B then the number of elements in a is less than or equal to the number of elements of B, so a better camparison might be between the subset symbol and the "less than or equal to" sumbol. One place wher there is a comparison is that if A is a subset of B and B is a subset of C then A is a subset of C. The same relationship is true with less than. If a is less than b and b is less than c then a is less than c.
  2. I am going to use the notation |D| to mean the number of elements in the set D and <= for "less than or equal to".

    The best you can say is that
    47 <= |AUB| <= 79
    0 <= |A intersect B| <= 32
    BUC = C so |BUC| = 32
    B intersect C is C so |B intersect C| = |C|

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