SOLUTION: first calculate the number of subsets for the​ set, then calculate the number of proper subsets. ​{ 19, 20, 0, 10 ​}

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Question 1145426: first calculate the number of subsets for the​ set, then calculate the number of proper subsets.
​{ 19, 20, 0, 10 ​}

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
For any set, the number of subsets is +2%5En+, where n=number of elements in the set

For the posted problem, there are 2%5E4+=+highlight%2816%29+ subsets.

One way to think about it: when forming a given subset, as you scan through the elements of the set, you can choose to (1) include that element in the subset or (2) exclude that element from the subset, hence each element multiplies by two the number of possible subsets.


The number of of proper subsets is +2%5En+-+1+ as each subset must contain elements from the set, but not contain ALL of the elements of the set. There is only one subset that has all the elements from the set, so the -1 subtracts that one out. For the posted problem, there are 15 proper subsets.