List all the subsets of the given set.
{tiger, muskrat, marmoset}
{}, {tiger}, {muskrat}, {marmoset}, {tiger, muskrat}, {tiger, marmoset}, {muskrat, marmoset}, {tiger, muskrat, marmoset}
To find all the subsets of the given set {tiger, muskrat, marmoset}, we need to consider all possible combinations of its elements.
Here are all the subsets of the given set:
1. Empty set: {}
2. Subset with one element: {tiger}, {muskrat}, {marmoset}
3. Subset with two elements: {tiger, muskrat}, {tiger, marmoset}, {muskrat, marmoset}
4. Subset with three elements: {tiger, muskrat, marmoset}
In total, there are 8 subsets of the given set.
To list all the subsets of a given set, you can use the power set method. Here's how you can do it for the set {tiger, muskrat, marmoset}:
1. Start by writing down the empty set: {}
This is one of the subsets.
2. Next, take each element of the set and create subsets with just that element.
- The subset {tiger} contains only the element tiger.
- The subset {muskrat} contains only the element muskrat.
- The subset {marmoset} contains only the element marmoset.
3. Now, take pairs of elements from the set and create subsets with those pairs.
- The subset {tiger, muskrat} contains both tiger and muskrat.
- The subset {tiger, marmoset} contains both tiger and marmoset.
- The subset {muskrat, marmoset} contains both muskrat and marmoset.
4. Finally, create a subset that contains all the elements of the original set.
- The subset {tiger, muskrat, marmoset} contains all three elements.
So, the complete list of subsets for the set {tiger, muskrat, marmoset} is:
{}, {tiger}, {muskrat}, {marmoset}, {tiger, muskrat}, {tiger, marmoset}, {muskrat, marmoset}, {tiger, muskrat, marmoset}