Quandaries and Queries Name: Susan Who is asking: Parent Level: All Question: 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, 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. 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| Penny Go to Math Central