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Part 1
List all the subsets of the given set.
{wolverine, camel, wildcat}
The subsets of the given set {wolverine, camel, wildcat} are:
1. {}
2. {wolverine}
3. {camel}
4. {wildcat}
5. {wolverine, camel}
6. {wolverine, wildcat}
7. {camel, wildcat}
8. {wolverine, camel, wildcat}
To list all the subsets of the set {wolverine, camel, wildcat}, we can use a systematic approach.
Step 1: Start with the empty set
{}
Step 2: Consider each element in the given set, one at a time.
2.1: Add the first element to the current subset
{wolverine}
2.2: Add the second element to the current subset
{wolverine, camel}
2.3: Add the third element to the current subset
{wolverine, camel, wildcat}
Step 3: Consider all possible combinations of 2 elements from the given set.
3.1: Combine the first and second elements
{wolverine, camel}
3.2: Combine the first and third elements
{wolverine, wildcat}
3.3: Combine the second and third elements
{camel, wildcat}
Step 4: Consider all possible combinations of 3 elements from the given set.
4.1: Combine all elements
{wolverine, camel, wildcat}
Step 5: Include the original set itself.
{wolverine, camel, wildcat}
Therefore, the subsets of the set {wolverine, camel, wildcat} are:
{}, {wolverine}, {camel}, {wildcat}, {wolverine, camel}, {wolverine, wildcat}, {camel, wildcat}, {wolverine, camel, wildcat}.
To find all the subsets of a given set, you can follow these steps:
1. Begin with an empty set and consider each element of the original set one by one.
2. For each element, generate new subsets by either including or excluding the current element.
3. Repeat this process until you have considered all elements of the set.
Let's apply these steps to the given set {wolverine, camel, wildcat}:
Step 1: Begin with an empty set: {}
Step 2: Consider the first element, "wolverine":
- Generate a new subset by including "wolverine": {wolverine}
- Generate a new subset by excluding "wolverine": {}
Step 3: Consider the second element, "camel":
- Generate a new subset by including "camel" in the previous subsets:
- Including "wolverine": {wolverine, camel}
- Excluding "wolverine": {camel}
- Generate a new subset by excluding "camel" in the previous subsets:
- Including "wolverine": {wolverine}
- Excluding "wolverine": {}
Step 4: Consider the third element, "wildcat":
- Generate a new subset by including "wildcat" in the previous subsets:
- Including "wolverine, camel": {wolverine, camel, wildcat}
- Excluding "wolverine, camel": {camel, wildcat}
- Including "wolverine": {wolverine, wildcat}
- Excluding "wolverine": {wildcat}
- Generate a new subset by excluding "wildcat" in the previous subsets:
- Including "wolverine, camel": {wolverine, camel}
- Excluding "wolverine, camel": {camel}
- Including "wolverine": {wolverine}
- Excluding "wolverine": {}
Thus, the subsets of the given set {wolverine, camel, wildcat} are:
{}, {wolverine}, {camel}, {camel, wildcat}, {wolverine, wildcat}, {wolverine, camel}, {wolverine, camel, wildcat}.