Step 1 :The given set is \(\{13,2,6,18,16\}\).
Step 2 :The number of elements in the set is 5.
Step 3 :The number of subsets of a set is given by the formula \(2^n\), where \(n\) is the number of elements in the set.
Step 4 :Substituting \(n = 5\) into the formula, we get \(2^5\) which equals 32.
Step 5 :So, the number of subsets for the given set is \(\boxed{32}\).
Step 6 :A proper subset is a subset that is not equal to the original set. So, to calculate the number of proper subsets, we subtract 1 from the total number of subsets.
Step 7 :Subtracting 1 from 32, we get 31.
Step 8 :So, the number of proper subsets is \(\boxed{31}\).