List the subsets of the set:
{5, 10, 15}
show your work
The subsets of the set {5, 10, 15} are:
1) Empty set {}
2) {5}
3) {10}
4) {15}
5) {5, 10}
6) {5, 15}
7) {10, 15}
8) {5, 10, 15}
To list all the subsets of the set {5, 10, 15}, we can follow these steps:
1. Start with an empty set: {}
2. Add each individual element as a separate subset: {5}, {10}, {15}
3. Add sets with combinations of two elements:
- {5, 10}
- {5, 15}
- {10, 15}
4. Finally, include the entire set as a subset: {5, 10, 15}
So, the subsets of the set {5, 10, 15} are:
{}, {5}, {10}, {15}, {5, 10}, {5, 15}, {10, 15}, {5, 10, 15}
To find all the subsets of a set, you can use the power set method. The power set of a set is a collection of all possible subsets of that set.
For the given set {5, 10, 15}, we can start by considering the empty set {} as the first subset. Then, for each element in the set, we can add it to the existing subsets and create new subsets.
Let's go step by step:
Step 1: Start with the empty set
{}
This represents the empty subset.
Step 2: Add the first element, 5
{}, {5}
We now have two subsets: an empty subset and a subset containing only the first element.
Step 3: Add the second element, 10
{}, {5}, {10}, {5, 10}
We add two new subsets to the previous ones: one containing only the second element and one containing the first and second elements.
Step 4: Add the third element, 15
{}, {5}, {10}, {5, 10}, {15}, {5, 15}, {10, 15}, {5, 10, 15}
We add four new subsets: one containing only the third element, two containing the second and third elements (in different combinations), and one containing all three elements.
So, the subsets of the set {5, 10, 15} are:
{}, {5}, {10}, {5, 10}, {15}, {5, 15}, {10, 15}, {5, 10, 15}
You can also verify this by counting the number of subsets. If a set has n elements, the total number of subsets is given by 2^n, including the empty set and the set itself. In this case, the set has 3 elements, so 2^3 = 8 subsets are expected, which is consistent with our list above.