Final answer:
The number of different subsets for the set A = {1,2,3,4} is 16, utilizing the formula 2 to the power of the number of elements. For the set A = {1,2,3,4,5}, there are 32 subsets and 31 proper subsets, as a proper subset cannot be the original set itself.
Step-by-step explanation:
Calculating the Number of Subsets and Proper Subsets
To find the number of different subsets for a set A = {1,2,3,4}, we utilize the formula 2n, where n is the number of elements in the set. In this case, A has 4 elements, so there are 24 = 16 different subsets of A.
For the set A = {1,2,3,4,5}, which contains 5 elements, there are 25 = 32 different subsets. Since a proper subset is a subset that is not equal to the original set, the number of proper subsets is one less than the total number of subsets. Therefore, there are 32 - 1 = 31 proper subsets of A.