For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets. (0,19,13,4)

Question

For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets.  (0,19,13,4)

Answer 1

The total number of subsets of a finite set is 2ⁿ, where n is the number of elements of the set.  So in this case it is 2⁴ = 16.

 

The only subset that is NOT a proper subset is the set itself.  It is a subset of itself, but not a proper subset.  So you have to subtract 1, to get 15 proper subsets.