Final answer:
The number of subsets of a set with n elements is found using the formula 2n. Each element has two possibilities, inclusion or exclusion, resulting in a total of 2n subsets, which includes the empty set and the set itself.
Step-by-step explanation:
To find the number of subsets of a given set with n elements, we use the formula 2n. This is because each element in the set can either be included or excluded from a subset, creating two possibilities for each element. When you have n elements, you multiply these possibilities together, which gives you 2 x 2 x 2... (n times), or 2n.
For example, if a set has 3 elements, then the total number of subsets is 23 which equals 8 subsets. These subsets include the empty subset, the set itself, and all possible combinations of the elements.
So, if a set has n elements, then the total number of subsets is 2n. This confirms the formula for finding the number of subsets for a given set.
To find the number of subsets of a given set, we need to use the concept of combinations. If a set has n elements, then the total number of subsets is 2^n.
For example, if a set has 3 elements, then the total number of subsets is 2^3 = 8. These subsets are: {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}.
So, if a set has n elements, the total number of subsets is 2^n.