Expert: Sherry Wallin - 4/21/2009

Question
1.  A 10-element set has ___ subsets.
2.  Also, set A has 15 proper subsets.  How many elements  are in Set A?

Answer
Angie~
   2^10 subsets is the answer to 1. It is always 2^(# of elements in A) for the number of subsets. You can choose a small number and check this. Try 3 elements a,b,c so there are 2^3 = 8 subsets:{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c},{}. Note the last two are called trivial and they are the ones that you omit for proper subsets. A proper subset is one where you don't count the whole set as a subset and the one where you don't count the empty set.
   For #2 you need to know what a proper subset is and just remember it is all the subsets that are not all of A. So 2^15 -1 (exclude A) is the number of subsets for #2.

Good luck,
Math Prof